Evaluate the two problems

Question

Evaluate

(a) ∫^((2pi)/4)₀ |sin(4x)|dx=______

(b) ∫^100pi₀|sin(4x)|dx=______

Answer 1

For (a) sub u=4x

Then integral becomes (1/4) integral of /sin u/ from 0 to 2 pi

Think about the sine graph, this is the same as 2 integral sin(u) from 0 to pi.

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For (b) sub u=4x

integral becomes 1/4 integral of /sin u/ from 0 to 400 pi

By periodicity of sine function this is 200 x result from (a)