Integrate int(100-x^2)dx

 Exercise

$\int\left(100-x^2\right)dx$

 

Expand the integral $\int\left(100-x^2\right)dx$ into $2$ integrals using the sum rule for integrals, to then solve each integral separately

$\int100dx+\int-x^2dx$

 

The integral $\int100dx$ results in: $100x$

$100x$

 

The integral $\int-x^2dx$ results in: $\frac{-x^{3}}{3}$

$\frac{-x^{3}}{3}$

 

Gather the results of all integrals

$100x+\frac{-x^{3}}{3}$

 

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

$100x+\frac{-x^{3}}{3}+C_0$

$100x+\frac{-x^{3}}{3}+C_0$

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