NZ Level 8 (NZC) Level 3 (NCEA) [In development]
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Integration of sin/cos (non-linear functions)

Interactive practice questions

Consider the function $y=\sin\left(x^5\right)$y=sin(x5).

a

Find the derivative $\frac{dy}{dx}$dydx.

b

Hence find the value of $\int x^4\cos\left(x^5\right)dx$x4cos(x5)dx.

You may use $C$C to represent the constant of integration.

Easy
Approx 2 minutes
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Consider the function $y=\cos\left(6x^2-\frac{\pi}{3}\right)$y=cos(6x2π3).

Determine the value of $\int_3^72\cos\left(2x+5\right)dx$732cos(2x+5)dx.

Give your answer correct to two decimal places.

Outcomes

M8-11

Choose and apply a variety of differentiation, integration, and antidifferentiation techniques to functions and relations, using both analytical and numerical methods

91579

Apply integration methods in solving problems

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