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Exam: CBSE Class 12
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Q226
#226
Mathematics → Integrals → Integrals of Special Forms
·
Easy
Add
Integrate the function
1
+
x
2
9
\sqrt{1 + \dfrac{x^2}{9}}
1
+
9
x
2
.
Show model answer
[QEx 7.7 Q9 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
Report
Q227
#227
Mathematics → Integrals → Integrals of Special Forms
·
Easy
Add
∫
1
+
x
2
d
x
\int \sqrt{1 + x^2}\,dx
∫
1
+
x
2
d
x
is equal to
A
x
2
1
+
x
2
+
1
2
log
∣
(
x
+
1
+
x
2
)
∣
+
C
\dfrac{x}{2}\sqrt{1 + x^2} + \dfrac{1}{2}\log\left|\left(x + \sqrt{1 + x^2}\right)\right| + C
2
x
1
+
x
2
+
2
1
lo
g
(
x
+
1
+
x
2
)
+
C
B
2
3
(
1
+
x
2
)
3
2
+
C
\dfrac{2}{3}(1 + x^2)^{\frac{3}{2}} + C
3
2
(
1
+
x
2
)
2
3
+
C
C
2
3
x
(
1
+
x
2
)
3
2
+
C
\dfrac{2}{3}x(1 + x^2)^{\frac{3}{2}} + C
3
2
x
(
1
+
x
2
)
2
3
+
C
D
x
2
2
1
+
x
2
+
1
2
x
2
log
∣
x
+
1
+
x
2
∣
+
C
\dfrac{x^2}{2}\sqrt{1 + x^2} + \dfrac{1}{2}x^2\log\left|x + \sqrt{1 + x^2}\right| + C
2
x
2
1
+
x
2
+
2
1
x
2
lo
g
x
+
1
+
x
2
+
C
Tap an option to check your answer.
[QEx 7.7 Q10 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
Report
Q228
#228
Mathematics → Integrals → Integrals of Special Forms
·
Moderate
Add
∫
x
2
−
8
x
+
7
d
x
\int \sqrt{x^2 - 8x + 7}\,dx
∫
x
2
−
8
x
+
7
d
x
is equal to
A
1
2
(
x
−
4
)
x
2
−
8
x
+
7
+
9
log
∣
x
−
4
+
x
2
−
8
x
+
7
∣
+
C
\dfrac{1}{2}(x - 4)\sqrt{x^2 - 8x + 7} + 9\log\left|x - 4 + \sqrt{x^2 - 8x + 7}\right| + C
2
1
(
x
−
4
)
x
2
−
8
x
+
7
+
9
lo
g
x
−
4
+
x
2
−
8
x
+
7
+
C
B
1
2
(
x
+
4
)
x
2
−
8
x
+
7
+
9
log
∣
x
+
4
+
x
2
−
8
x
+
7
∣
+
C
\dfrac{1}{2}(x + 4)\sqrt{x^2 - 8x + 7} + 9\log\left|x + 4 + \sqrt{x^2 - 8x + 7}\right| + C
2
1
(
x
+
4
)
x
2
−
8
x
+
7
+
9
lo
g
x
+
4
+
x
2
−
8
x
+
7
+
C
C
1
2
(
x
−
4
)
x
2
−
8
x
+
7
−
3
2
log
∣
x
−
4
+
x
2
−
8
x
+
7
∣
+
C
\dfrac{1}{2}(x - 4)\sqrt{x^2 - 8x + 7} - 3\sqrt{2}\log\left|x - 4 + \sqrt{x^2 - 8x + 7}\right| + C
2
1
(
x
−
4
)
x
2
−
8
x
+
7
−
3
2
lo
g
x
−
4
+
x
2
−
8
x
+
7
+
C
D
1
2
(
x
−
4
)
x
2
−
8
x
+
7
−
9
2
log
∣
x
−
4
+
x
2
−
8
x
+
7
∣
+
C
\dfrac{1}{2}(x - 4)\sqrt{x^2 - 8x + 7} - \dfrac{9}{2}\log\left|x - 4 + \sqrt{x^2 - 8x + 7}\right| + C
2
1
(
x
−
4
)
x
2
−
8
x
+
7
−
2
9
lo
g
x
−
4
+
x
2
−
8
x
+
7
+
C
Tap an option to check your answer.
[QEx 7.7 Q11 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Set · 4 questions
Evaluate the following integrals:
Q229
#229
Mathematics → Integrals → Definite Integrals and the Fundamental Theorem
·
Easy
Add
Evaluate
∫
2
3
x
2
d
x
\int_{2}^{3} x^{2}\,dx
∫
2
3
x
2
d
x
.
Show model answer
[Q7.8 Eg.25(i) · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q230
#230
Mathematics → Integrals → Definite Integrals and the Fundamental Theorem
·
Hard
Add
Evaluate
∫
4
9
x
(
30
−
x
3
2
)
2
d
x
\int_{4}^{9} \frac{\sqrt{x}}{\left(30 - x^{\frac{3}{2}}\right)^{2}}\,dx
∫
4
9
(
30
−
x
2
3
)
2
x
d
x
.
Show model answer
[Q7.8 Eg.25(ii) · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q231
#231
Mathematics → Integrals → Definite Integrals and the Fundamental Theorem
·
Moderate
Add
Evaluate
∫
1
2
x
d
x
(
x
+
1
)
(
x
+
2
)
\int_{1}^{2} \frac{x\,dx}{(x+1)(x+2)}
∫
1
2
(
x
+
1
)
(
x
+
2
)
x
d
x
.
Show model answer
[Q7.8 Eg.25(iii) · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
Report
Q232
#232
Mathematics → Integrals → Definite Integrals and the Fundamental Theorem
·
Moderate
Add
Evaluate
∫
0
π
4
sin
3
2
t
cos
2
t
d
t
\int_{0}^{\frac{\pi}{4}} \sin^{3} 2t \cos 2t \,dt
∫
0
4
π
sin
3
2
t
cos
2
t
d
t
.
Show model answer
[Q7.8 Eg.25(iv) · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
Report
Q233
#233
Mathematics → Integrals → Definite Integrals and the Fundamental Theorem
·
Easy
Add
Evaluate the definite integral
∫
−
1
1
(
x
+
1
)
d
x
\int_{-1}^{1} (x+1)\,dx
∫
−
1
1
(
x
+
1
)
d
x
.
Show model answer
[QEx 7.8 Q1 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q234
#234
Mathematics → Integrals → Definite Integrals and the Fundamental Theorem
·
Easy
Add
Evaluate the definite integral
∫
2
3
1
x
d
x
\int_{2}^{3} \frac{1}{x}\,dx
∫
2
3
x
1
d
x
.
Show model answer
[QEx 7.8 Q2 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
Report
Q235
#235
Mathematics → Integrals → Definite Integrals and the Fundamental Theorem
·
Easy
Add
Evaluate the definite integral
∫
1
2
(
4
x
3
−
5
x
2
+
6
x
+
9
)
d
x
\int_{1}^{2} (4x^{3} - 5x^{2} + 6x + 9)\,dx
∫
1
2
(
4
x
3
−
5
x
2
+
6
x
+
9
)
d
x
.
Show model answer
[QEx 7.8 Q3 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q236
#236
Mathematics → Integrals → Definite Integrals and the Fundamental Theorem
·
Easy
Add
Evaluate the definite integral
∫
0
π
4
sin
2
x
d
x
\int_{0}^{\frac{\pi}{4}} \sin 2x \,dx
∫
0
4
π
sin
2
x
d
x
.
Show model answer
[QEx 7.8 Q4 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q237
#237
Mathematics → Integrals → Definite Integrals and the Fundamental Theorem
·
Easy
Add
Evaluate the definite integral
∫
0
π
2
cos
2
x
d
x
\int_{0}^{\frac{\pi}{2}} \cos 2x \,dx
∫
0
2
π
cos
2
x
d
x
.
Show model answer
[QEx 7.8 Q5 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q238
#238
Mathematics → Integrals → Definite Integrals and the Fundamental Theorem
·
Easy
Add
Evaluate the definite integral
∫
4
5
e
x
d
x
\int_{4}^{5} e^{x}\,dx
∫
4
5
e
x
d
x
.
Show model answer
[QEx 7.8 Q6 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q239
#239
Mathematics → Integrals → Definite Integrals and the Fundamental Theorem
·
Moderate
Add
Evaluate the definite integral
∫
0
π
4
tan
x
d
x
\int_{0}^{\frac{\pi}{4}} \tan x \,dx
∫
0
4
π
tan
x
d
x
.
Show model answer
[QEx 7.8 Q7 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q240
#240
Mathematics → Integrals → Definite Integrals and the Fundamental Theorem
·
Moderate
Add
Evaluate the definite integral
∫
π
6
π
4
cosec
x
d
x
\int_{\frac{\pi}{6}}^{\frac{\pi}{4}} \operatorname{cosec} x \,dx
∫
6
π
4
π
cosec
x
d
x
.
Show model answer
[QEx 7.8 Q8 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q241
#241
Mathematics → Integrals → Definite Integrals and the Fundamental Theorem
·
Easy
Add
Evaluate the definite integral
∫
0
1
d
x
1
−
x
2
\int_{0}^{1} \frac{dx}{\sqrt{1 - x^{2}}}
∫
0
1
1
−
x
2
d
x
.
Show model answer
[QEx 7.8 Q9 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
Report
Q242
#242
Mathematics → Integrals → Definite Integrals and the Fundamental Theorem
·
Easy
Add
Evaluate the definite integral
∫
0
1
d
x
1
+
x
2
\int_{0}^{1} \frac{dx}{1 + x^{2}}
∫
0
1
1
+
x
2
d
x
.
Show model answer
[QEx 7.8 Q10 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
Report
Q243
#243
Mathematics → Integrals → Definite Integrals and the Fundamental Theorem
·
Moderate
Add
Evaluate the definite integral
∫
2
3
d
x
x
2
−
1
\int_{2}^{3} \frac{dx}{x^{2} - 1}
∫
2
3
x
2
−
1
d
x
.
Show model answer
[QEx 7.8 Q11 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
Report
Q244
#244
Mathematics → Integrals → Definite Integrals and the Fundamental Theorem
·
Moderate
Add
Evaluate the definite integral
∫
0
π
2
cos
2
x
d
x
\int_{0}^{\frac{\pi}{2}} \cos^{2} x \,dx
∫
0
2
π
cos
2
x
d
x
.
Show model answer
[QEx 7.8 Q12 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q245
#245
Mathematics → Integrals → Definite Integrals and the Fundamental Theorem
·
Moderate
Add
Evaluate the definite integral
∫
2
3
x
d
x
x
2
+
1
\int_{2}^{3} \frac{x\,dx}{x^{2} + 1}
∫
2
3
x
2
+
1
x
d
x
.
Show model answer
[QEx 7.8 Q13 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q246
#246
Mathematics → Integrals → Definite Integrals and the Fundamental Theorem
·
Moderate
Add
Evaluate the definite integral
∫
0
1
2
x
+
3
5
x
2
+
1
d
x
\int_{0}^{1} \frac{2x + 3}{5x^{2} + 1}\,dx
∫
0
1
5
x
2
+
1
2
x
+
3
d
x
.
Show model answer
[QEx 7.8 Q14 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q247
#247
Mathematics → Integrals → Definite Integrals and the Fundamental Theorem
·
Moderate
Add
Evaluate the definite integral
∫
0
1
x
e
x
2
d
x
\int_{0}^{1} x\, e^{x^{2}}\,dx
∫
0
1
x
e
x
2
d
x
.
Show model answer
[QEx 7.8 Q15 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q248
#248
Mathematics → Integrals → Definite Integrals and the Fundamental Theorem
·
Hard
Add
Evaluate the definite integral
∫
1
2
5
x
2
x
2
+
4
x
+
3
d
x
\int_{1}^{2} \frac{5x^{2}}{x^{2} + 4x + 3}\,dx
∫
1
2
x
2
+
4
x
+
3
5
x
2
d
x
.
Show model answer
[QEx 7.8 Q16 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
Report
Q249
#249
Mathematics → Integrals → Definite Integrals and the Fundamental Theorem
·
Moderate
Add
Evaluate the definite integral
∫
0
π
4
(
2
sec
2
x
+
x
3
+
2
)
d
x
\int_{0}^{\frac{\pi}{4}} (2\sec^{2} x + x^{3} + 2)\,dx
∫
0
4
π
(
2
sec
2
x
+
x
3
+
2
)
d
x
.
Show model answer
[QEx 7.8 Q17 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
Report
Q250
#250
Mathematics → Integrals → Definite Integrals and the Fundamental Theorem
·
Moderate
Add
Evaluate the definite integral
∫
0
π
(
sin
2
x
2
−
cos
2
x
2
)
d
x
\int_{0}^{\pi} \left(\sin^{2}\frac{x}{2} - \cos^{2}\frac{x}{2}\right)\,dx
∫
0
π
(
sin
2
2
x
−
cos
2
2
x
)
d
x
.
Show model answer
[QEx 7.8 Q18 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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