$$\int_5^{10}\left(4x-8\right)dx$$  

STEP 1:

What's the antiderivative of $$4x-8$$ ?

(no need to write down the +C)

$$\int_5^{10}\left(4x-8\right)dx=\left[2x^2-8x\right]_5^{10}$$  

STEP 2:

Evaluate the antiderivative at the upper limit.

$$\int_5^{10}\left(4x-8\right)dx=\left[2x^2-8x\right]_5^{10}$$  

STEP 3:

Evaluate the antiderivative at the lower limit.

$$\int_5^{10}\left(4x-8\right)dx=\left[2x^2-8x\right]_5^{10}$$  

STEP 4:

Final answer. Subtract answer in step 3 from answer in step 2.

$$\int_{-2}^{-1}\left(7x^{-3}\right)dx$$

STEP 1:

What's the antiderivative of $$7x^{-3}$$ ?

(no need to write down the +C)

$$\int_{-2}^{-1}\left(7x^{-3}\right)dx=\left[\frac{7x^{-2}}{-2}\right]_{-2}^{-1}$$

STEP 2:

Evaluate the antiderivative at the upper limit.

(write your answer as a fraction, not a decimal number)

$$\int_{-2}^{-1}\left(7x^{-3}\right)dx=\left[\frac{7x^{-2}}{-2}\right]_{-2}^{-1}$$

STEP 3:

Evaluate the antiderivative at the lower limit.

(write your answer as a fraction, not a decimal number)

$$\int_{-2}^{-1}\left(7x^{-3}\right)dx=\left[\frac{7x^{-2}}{-2}\right]_{-2}^{-1}$$

STEP 4:

Final answer. Subtract answer in step 3 from answer in step 2.

Evaluate the definite integral.

(do not round up your intermediate computations; use three decimals in your final answer without rounding)

$$\int_0^5\left(e^{\frac{x}{2}}\right)dx$$

$$\int_0^{-8}\left(2\sqrt[3]{x}\right)dx$$

STEP 1:

What's the antiderivative of $$2\sqrt[3]{x}$$ ?

(no need to write down the +C)

$$\int_0^{-8}\left(2\sqrt[3]{x}\right)dx=\left[\frac{2x^{\frac{4}{3}}}{\frac{4}{3}}\right]_0^{-8}$$

STEP 2:

Evaluate the antiderivative at the upper limit.

$$\int_0^{-8}\left(2\sqrt[3]{x}\right)dx=\left[\frac{2x^{\frac{4}{3}}}{\frac{4}{3}}\right]_0^{-8}$$

STEP 3:

Evaluate the antiderivative at the lower limit.

$$\int_0^{-8}\left(2\sqrt[3]{x}\right)dx=\left[\frac{2x^{\frac{4}{3}}}{\frac{4}{3}}\right]_0^{-8}$$

STEP 4:

Final answer. Subtract answer in step 3 from answer in step 2.

Evaluate the definite integral.

(do not round up your intermediate computations; use three decimals in your final answer without rounding)

$$\int_{0.1}^{10}\left(\frac{1}{x}\right)dx$$

$$\int_0^3\left(-x^4+3x^3\right)dx$$

STEP 2:

What's the antiderivative of $$-x^4+3x^3$$ ?

(no need to write down the +C)

$$\int_0^3\left(-x^4+3x^3\right)dx=\left[-\frac{x^5}{5}+\frac{3x^4}{4}\right]_0^3$$

STEP 3:

Evaluate the antiderivative at the upper limit.

$$\int_0^3\left(-x^4+3x^3\right)dx=\left[-\frac{x^5}{5}+\frac{3x^4}{4}\right]_0^3$$

STEP 4:

Evaluate the antiderivative at the lower limit.

$$\int_0^3\left(-x^4+3x^3\right)dx=\left[-\frac{x^5}{5}+\frac{3x^4}{4}\right]_0^3$$

STEP 5:

Final answer. Subtract answer in step 4 from answer in step 3.

Evaluate the definite integral.

(do not round up your intermediate computations; use three decimals in your final answer without rounding)

$$\int_9^9\left(\sqrt[]{4-x^2}\right)dx$$