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Find the upper limit a when the value of the definite integral is given

This type of question, asked 4 times: 11 Apr 2026 S1, 11 Apr 2026 S2, 13 Apr 2026 S1, 13 Apr 2026 S2. All 4 questions below, oldest first.

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  1. Question 1

    11 Apr 2026 S1

    82
    If ∫1a(2x+1) dx=5\displaystyle\int_1^a(2x + 1)\,dx = 5, then the sum of the values of aa is..

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  2. Question 2

    11 Apr 2026 S2

    82
    If ∫0k11+4x dx=log⁡2(43)\displaystyle\int_0^k\dfrac{1}{1 + 4^x}\,dx = \log_2\left(\dfrac{4}{3}\right), then k=k = _____

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  3. Question 3

    13 Apr 2026 S1

    80
    If ∫0adx1+4x2=π8\displaystyle\int_0^a\dfrac{dx}{1 + 4x^2} = \dfrac{\pi}{8}, then a=a =

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  4. Question 4

    13 Apr 2026 S2

    81
    If ∫0a(x2−4x+1) dx=6\int_0^a(x^2 - 4x + 1)\,dx = 6, then the real value of aa is

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