Integration by recognition and trigonometric identities

Integration by recognition and trigonometric identities Quiz

Spec 5.2 · Edexcel International A Level Maths: Quiz

Studying this course? Keep your progress in one place.

Pick an answer for each. Quizzes never use energy.

5 questions, one answer each

Each answer is checked as you go, with why.

See all 5 questions

  1. 1. Find ∫2xx2+1 dx\int\frac{2x}{x^2+1}\,dx.

    • A. 1(x2+1)2+c\frac{1}{(x^2+1)^2}+c
    • B. 2ln⁡(x2+1)+c2\ln(x^2+1)+c
    • C. ln⁡(x2+1)+c\ln(x^2+1)+c
    • D. 12ln⁡(x2+1)+c\frac12\ln(x^2+1)+c

  2. 2. Find ∫tan⁡x dx\int\tan x\,dx for 0<x<π20<x<\frac\pi2.

    • A. −ln⁡cos⁡x+c-\ln\cos x+c
    • B. ln⁡cos⁡x+c\ln\cos x+c
    • C. sec⁡2x+c\sec^2x+c
    • D. ln⁡sin⁡x+c\ln\sin x+c

  3. 3. Find ∫sec⁡22x dx\int\sec^22x\,dx.

    • A. 2tan⁡2x+c2\tan2x+c
    • B. tan⁡2x+c\tan2x+c
    • C. sec⁡2xtan⁡2x+c\sec2x\tan2x+c
    • D. 12tan⁡2x+c\frac12\tan2x+c

  4. 4. Find ∫sin⁡2x dx\int\sin^2x\,dx.

    • A. 13sin⁡3x+c\frac13\sin^3x+c
    • B. x2−sin⁡2x4+c\frac x2-\frac{\sin2x}{4}+c
    • C. x2+sin⁡2x4+c\frac x2+\frac{\sin2x}{4}+c
    • D. −12cos⁡2x+c-\frac12\cos^2x+c

  5. 5. Find ∫2(2x−1)4 dx\int\frac{2}{(2x-1)^4}\,dx.

    • A. −8(2x−1)5+c-\frac{8}{(2x-1)^5}+c
    • B. 1(2x−1)3+c\frac{1}{(2x-1)^3}+c
    • C. −13(2x−1)3+c-\frac{1}{3(2x-1)^3}+c
    • D. −23(2x−1)3+c-\frac{2}{3(2x-1)^3}+c

Quiz