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Find f(x) from f'(x) and one given value of f

This type of question, asked 4 times: 10 May 2023 S2, 9 May 2024 S2, 17 Apr 2026 S1, 13 May 2026 S2. All 4 questions below, oldest first.

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  1. Question 1

    10 May 2023 S2

    137
    If ddxf(x)=4x3−3x4\frac{d}{dx}f(x) = 4x^3 - \frac{3}{x^4} such that f(2)=0f(2) = 0, then f(x)f(x) is equal to

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  2. Question 2

    9 May 2024 S2

    109
    If f′(x)=x−5x5f'(x) = x - \dfrac{5}{x^5} and f(1)=4f(1) = 4, then f(x)f(x) is

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  3. Question 3

    17 Apr 2026 S1

    82
    If f′(x)=(x+1)exxf'(x) = \dfrac{(\sqrt{x} + 1)e^{\sqrt{x}}}{\sqrt{x}} and f(0)=ef(0) = e then f(1)=…………f(1) = \ldots\ldots\ldots\ldots

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  4. Question 4

    13 May 2026 S2

    79
    If f′(x)=k(cos⁡x−sin⁡x),f′(0)=5,f(π2)=19f'(x) = k(\cos x - \sin x), f'(0) = 5, f\left(\dfrac{\pi}{2}\right) = 19, Then f(x)=f(x) =

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