Solve the trigonometric integral int(7sin(x)^2)dx

 Exercise

$\int7sen^2\:x\:dx$

 

The integral of a function times a constant ($7$) is equal to the constant times the integral of the function

$7\int\sin\left(x\right)^2dx$

 

Apply the formula: $\int\sin\left(\theta \right)^2dx$$=\frac{1}{2}\theta -\frac{1}{4}\sin\left(2\theta \right)+C$

$7\left(\frac{1}{2}x-\frac{1}{4}\sin\left(2x\right)\right)$

 

As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration $C$

$7\left(\frac{1}{2}x-\frac{1}{4}\sin\left(2x\right)\right)+C_0$

 

Expand and simplify

$\frac{7}{2}x-\frac{7}{4}\sin\left(2x\right)+C_0$

$\frac{7}{2}x-\frac{7}{4}\sin\left(2x\right)+C_0$

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