Reduction formulae

Reduction formulae Quiz

Spec 2.1 · Edexcel A-Level Further Maths: Quiz

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5 questions, one answer each

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  1. 1. If In=∫0π2sin⁡nx dxI_n=\int_0^{\frac{\pi}{2}}\sin^nx\,dx, express I6I_6 in terms of I4I_4.

    • A. 56I4\frac56I_4
    • B. 65I4\frac65I_4
    • C. 16I4\frac16I_4
    • D. 45I4\frac45I_4

  2. 2. Find ∫0π2sin⁡3x dx\int_0^{\frac{\pi}{2}}\sin^3x\,dx.

    • A. 13\frac13
    • B. 11
    • C. 23\frac23
    • D. π4\frac{\pi}{4}

  3. 3. Given Jn=e−nJn−1J_n=e-nJ_{n-1} and J1=1J_1=1, find J2J_2.

    • A. e−1e-1
    • B. e−2e-2
    • C. 2e−12e-1
    • D. e+2e+2

  4. 4. Using In+2=In+2sin⁡((n+1)x)n+1I_{n+2}=I_n+\frac{2\sin((n+1)x)}{n+1} with n=3n=3, the extra term is

    • A. sin⁡4x2\frac{\sin4x}{2}
    • B. 2sin⁡3x3\frac{2\sin3x}{3}
    • C. 2sin⁡5x5\frac{2\sin5x}{5}
    • D. sin⁡4x4\frac{\sin4x}{4}

  5. 5. Find ∫0π4tan⁡2x dx\int_0^{\frac{\pi}{4}}\tan^2x\,dx.

    • A. π4\frac{\pi}{4}
    • B. π4−1\frac{\pi}{4}-1
    • C. 12\frac12
    • D. 1−π41-\frac{\pi}{4}

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