Solve ∫ (from 0 to 1) of 2sinθcosθ

$$\int _ { 0 } ^ { 1 } 2 \sin \theta \cos \theta$$

Evaluate

$$\sin(2\theta )$$

Solution Steps

Evaluate the indefinite integral first.

$$\int \frac{1}{2}\times 2\sin(2\theta )\mathrm{d}x$$

Find the integral of \frac{1}{2}\times 2\sin(2\theta ) using the table of common integrals rule \int a\mathrm{d}x=ax.

$$\frac{1}{2}\times 2x\sin(2\theta )$$

The definite integral is the antiderivative of the expression evaluated at the upper limit of integration minus the antiderivative evaluated at the lower limit of integration.

$$2\sin(\theta )\cos(\theta )+0\times 2\sin(\theta )\cos(\theta )$$

Simplify.

$$\sin(2\theta )$$

Differentiate w.r.t. θ

$$2\cos(2\theta )$$