Calculus of Trigonometric Functions

NZ Level 8 (NZC) Level 3 (NCEA) [In development]

Integration of sin/cos (non-linear functions)

Consider the function $y=\sin\left(x^5\right)$`y`=`s``i``n`(`x`5).

a

Find the derivative $\frac{dy}{dx}$`d``y``d``x`.

b

Hence find the value of $\int x^4\cos\left(x^5\right)dx$∫`x`4`c``o``s`(`x`5)`d``x`.

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

Easy

Approx 2 minutes

Sign up to try all questions

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

Apply integration methods in solving problems