Chapter 7.1, Problem 58PS

To determine

To find: The value of integral ${\displaystyle \int 2\sin \left(x\right)\cos \left(x\right)dx}$ by substituting $\cos \left(x\right)=u$ .

To determine

To find: The value of integral ${\displaystyle \int 2\sin \left(x\right)\cos \left(x\right)dx}$ by substituting $\sin \left(x\right)=u$ .

To determine

To find: The value of integral ${\displaystyle \int 2\sin \left(x\right)\cos \left(x\right)dx}$ by substituting the formula $2\sin \left(x\right)\cos \left(x\right)=\sin \left(2x\right)$ .

To determine

To show: The results obtained from the integral ${\displaystyle \int 2\sin \left(x\right)\cos \left(x\right)dx}$ in parts (a), (b) and (c) are same.