Solve ∫ (from - 2 to 1) of 3x^5

$$\int _ { - 2 } ^ { 1 } 3 x ^ { 5 }$$

Evaluate

$$-\frac{63}{2}=-31.5$$

Solution Steps

Evaluate the indefinite integral first.

$$\int 3x^{5}\mathrm{d}x$$

Factor out the constant using \int af\left(x\right)\mathrm{d}x=a\int f\left(x\right)\mathrm{d}x.

$$3\int x^{5}\mathrm{d}x$$

Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int x^{5}\mathrm{d}x with \frac{x^{6}}{6}. Multiply 3 times \frac{x^{6}}{6}.

$$\frac{x^{6}}{2}$$

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.

$$\frac{1^{6}}{2}-\frac{\left(-2\right)^{6}}{2}$$

Simplify.

$$-\frac{63}{2}$$