CBSE Class 12 Maths

Application of Integrals

Each concept is a short lesson, then questions until you get three right.

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4 concepts, a short lesson each

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Area between a curve and the X-axis

The area between $y = f(x)$ , the X-axis and $x = a$ , $x = b$ is $\int_a^b |y|\,dx$ ; a part below the axis gives a negative integral, so take its size

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Area between a curve and the X-axisThe area between $y = f(x)$ , the X-axis and $x = a$ , $x = b$ is $\int_a^b |y|\,dx$ ; a part below the axis gives a negative integral, so take its sizeStart
Area between a curve and the Y-axisBetween $x = g(y)$ , the Y-axis and $y = c$ , $y = d$ , the area is $\int_c^d |x|\,dy$ : integrate along $y$ with horizontal stripsStart
Areas of circles, ellipses and parabolasUse symmetry: find one quarter and multiply; the ellipse $\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1$ encloses $\pi ab$ , using $\int_0^a \sqrt{a^2 - x^2}\,dx = \dfrac{\pi a^2}{4}$ Start
Area between two curvesFind where the curves meet, then integrate (upper $-$ lower) $dx$ between those points, or (right $-$ left) $dy$ Start

Practise Application of Integrals

Once the concepts click, try the questions your exam asks.

Textbook exercisesEvery exercise, with model answers Past board questionsAsked from this chapter, with solutions

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Practise Application of Integrals