Question

Integration of sinx cosx dx . Ans is -cos2x/4+c. Solve by step.​

Answer 1

Explanation:

To solve ∫ sin x cos x dx, let us first simplify sin x cos x, using the trigonometric identity sin(2x) = 2 sin x cos x

⇒ sin x cos x = sin(2x) / 2

Now, using the simplified value for sin x cos x, the integral converts to:

∫ sin x cos x dx = ∫ sin (2x) / 2 dx = 1/2 ∫sin(2x) dx

We know that ∫ sin (ax) dx = -(1/a) cos ax + C, where C is the constant of integration

∫ sin x cos x = 1/2 ∫sin(2x) dx = −1/4 cos(2x) + C

Thus, the final integral of sin x.cos x is −1/4 cos(2x) + C