Solve ∫ (from - 4 to 4) of (y^3-35/2y)

$$\int _ { - 4 } ^ { 4 } ( y ^ { 3 } - \frac { 35 } { 2 } y )$$

Evaluate

$$8y^{3}-140y$$

Solution Steps

Evaluate the indefinite integral first.

$$\int y^{3}-\frac{35y}{2}\mathrm{d}x$$

Find the integral of y^{3}-\frac{35y}{2} using the table of common integrals rule \int a\mathrm{d}x=ax.

$$\left(y^{3}-\frac{35y}{2}\right)x$$

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.

$$\left(y^{3}-\frac{35}{2}y\right)\times 4-\left(y^{3}-\frac{35}{2}y\right)\left(-4\right)$$

Simplify.

$$8y^{3}-140y$$

Differentiate w.r.t. y

$$24y^{2}-140$$