Evaluate the Integral integral of 2sin(2x) with respect to x

Problem

(∫_^)(2*sin(2*x)*d(x))

Solution

1. Identify the constant and move it outside the integral.

(∫_^)(2*sin(2*x)*d(x))=2*(∫_^)(sin(2*x)*d(x))

2. Apply the integration rule for sin(a*x) which states that (∫_^)(sin(a*x)*d(x))=−1/a*cos(a*x)+C

a=2

3. Substitute the value of a into the formula.

2*(∫_^)(sin(2*x)*d(x))=2*(−1/2*cos(2*x))+C

4. Simplify the expression by multiplying the constants.

2*(−1/2)=−1

Final Answer

(∫_^)(2*sin(2*x)*d(x))=−cos(2*x)+C

Want more problems? Check here!