Question

QD: Using graphs and symmetry, approximate the integral of

i) sin(3x)*sin(1x) from x= -pi to pi.

Ii) sin(0x)*sin(0x) from x= -pi to pi

Iii) cos(0x)*cos(0x) from x= -pi to pi

iv) what slightly weird thing happened?

Answer 1

For the first part graph is:

2- (п, 0) 4 0 (-л, 0) -2

The curve is symmetric about y axis.

So, it shows that the given function is even

So, the integral will be for 0 to pi.

and putting limits we get:

25sin4r) sin(3r)sinzdx (cos2x cos4x)dx (.5sin2x 7

.5-.25= .25