Solve ∫ (from 6 to 181) of n+2y^2

$$\int _ { 6 } ^ { 181 } n + 2 y ^ { 2 }$$

Evaluate

$$175\left(2y^{2}+n\right)$$

Solution Steps

Evaluate the indefinite integral first.

$$\int n+2y^{2}\mathrm{d}x$$

Find the integral of n+2y^{2} using the table of common integrals rule \int a\mathrm{d}x=ax.

$$\left(n+2y^{2}\right)x$$

The definite integral is the antiderivative of the expression evaluated at the upper limit of integration minus the antiderivative evaluated at the lower limit of integration.

$$\left(n+2y^{2}\right)\times 181-\left(n+2y^{2}\right)\times 6$$

Simplify.

$$350y^{2}+175n$$

Differentiate w.r.t. n

$$175$$