Integration by Parts (Edexcel A-Level Mathematics): Quizzes

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Integration by Parts
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When should integration by parts be used?

Product of unrelated functions

What is the integration by parts formula?

∫udvdxdx=uv−∫vdudxdx\int u \frac{dv}{dx} dx = uv - \int v \frac{du}{dx} dx

Which differentiation rule is used to derive the integration by parts formula?

Product rule

Why can't ln⁡(x)\ln(x) be chosen as dvdx\frac{dv}{dx} in integration by parts?

ln⁡(x)\ln(x) can't be directly integrated

For ∫xsin⁡xdx\int x \sin x dx, what should uu be?

xx

What is ∫xexdx\int xe^x dx?

xex−ex+Cxe^x - e^x + C

How is ∫ln⁡xdx\int \ln x dx rewritten to use integration by parts?

∫1×ln⁡xdx\int 1 \times \ln x dx

What is ∫ln⁡xdx\int \ln x dx?

xln⁡x−x+cx \ln x - x + c

For ∫x2cos⁡xdx\int x^2 \cos x dx, how many times is integration by parts needed?

Twice

What is the exact value of ∫12xexdx\int_1^2 xe^x dx?

e2e^2

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