Which of the following is a step in evaluating
�ç(integer sign) cos^2 5x dx
A.�ç(integer sign) 1 + cos 10x / 2 dx
B.�ç(integer sign) 1 - cos 10x / 2 dx
C.�ç(integer sign) 1 + cos 10x / 20 dx
D.�ç(integer sign) 1 - cos 10x / 20 dx
A <<
Correct.
A.
∫(1 + cos(10x))/2 dx
using
cos(a)cos(b)=(1/2)(cos(a-b)+cos(a+b))
Thank you.
To determine which of the given options is a step in evaluating ∫(integer sign) cos^2(5x) dx, we can simplify the given equation.
Using the identity cos^2(x) = (1 + cos(2x))/2, we can rewrite the integral as:
∫(integer sign) (1 + cos(2(5x)))/2 dx
This can be further simplified as:
∫(integer sign) (1 + cos(10x))/2 dx
Comparing the simplified integral with the given options, we find that option A, ∫(integer sign) (1 + cos(10x))/2 dx, matches the simplified expression.
Therefore, option A is the correct step in evaluating ∫(integer sign) cos^2(5x) dx.