5.10 Indefinite integrals and substitution

5.10 Indefinite integrals and substitution Quiz

IB Maths: Analysis and Approaches SL: Quiz

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5 questions, one answer each

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  1. 1. Find ∫(6x2−4x−3) dx\displaystyle\int(6x^{2}-4x^{-3})\,dx.

    • A. 2x3+2x−2+C2x^{3}+2x^{-2}+C
    • B. 2x3−2x−2+C2x^{3}-2x^{-2}+C
    • C. 12x+12x−4+C12x+12x^{-4}+C
    • D. 3x3+x−4+C3x^{3}+x^{-4}+C

  2. 2. Find ∫e4x−1 dx\displaystyle\int e^{4x-1}\,dx.

    • A. 4e4x−1+C4e^{4x-1}+C
    • B. e4x−1+Ce^{4x-1}+C
    • C. 14e4x−1+C\dfrac14e^{4x-1}+C
    • D. e4x4x−1+C\dfrac{e^{4x}}{4x-1}+C

  3. 3. Find ∫3x dx\displaystyle\int\frac{3}{x}\,dx for x>0x>0.

    • A. 3ln⁡x+C3\ln x+C
    • B. −3x2+C-\dfrac{3}{x^{2}}+C
    • C. ln⁡3x+C\ln3x+C
    • D. 3x00+C\dfrac{3x^{0}}{0}+C

  4. 4. Find ∫3x2cos⁡(x3) dx\displaystyle\int3x^{2}\cos(x^{3})\,dx.

    • A. −sin⁡(x3)+C-\sin(x^{3})+C
    • B. sin⁡(x3)+C\sin(x^{3})+C
    • C. 3sin⁡(x3)+C3\sin(x^{3})+C
    • D. x3sin⁡(x3)+Cx^{3}\sin(x^{3})+C

  5. 5. dydx=cos⁡x\dfrac{dy}{dx}=\cos x and y=3y=3 when x=0x=0. Find yy.

    • A. y=sin⁡xy=\sin x
    • B. y=−sin⁡x+3y=-\sin x+3
    • C. y=sin⁡x+2y=\sin x+2
    • D. y=sin⁡x+3y=\sin x+3

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