Question

Evalute this integral

Answer 1

Answer:

(1/2)sin(2x) + C

Step-by-step explanation:

$y=2x\\\frac{dy}{dx} =2\\\ dx=\frac{dy}{2} \\\int\limits {cos 2x} \, dx \\\int\limits {cos(y) } \, \frac{dy}{2} =\frac{1}{2} \\\int\limits {cos(y) } \, dy=\frac{1}{2}sin(y) \\ substitute / y=2x\\\int\limits {cos 2x} \, dx = \frac{1}{2}sin(2x) +C$