(P3T7Q) Areas [CLASS//QUIZIZZ]

(P3T7Q) Areas [CLASS//QUIZIZZ]

Multiple Steps

Math Response

$$\int_5^{10}\left(4x-8\right)dx$$  

STEP 1:

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

(no need to write down the +C)

Type answer here

Correct Answer: 2x^2-8x

Deg^°

Rad

Math Response

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

STEP 2:

Evaluate the antiderivative at the upper limit.

Type answer here

Correct Answer: 120

Deg^°

Rad

Math Response

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

STEP 3:

Evaluate the antiderivative at the lower limit.

Type answer here

Correct Answer: 10

Deg^°

Rad

Math Response

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

STEP 4:

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

Type answer here

Correct Answer: 110

Deg^°

Rad

Multiple Steps

Math Response

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

STEP 1:

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

(no need to write down the +C)

Type answer here

Correct Answer: \frac{7x^{-2}}{-2}

Deg^°

Rad

Math Response

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

STEP 2:

Evaluate the antiderivative at the upper limit.

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

Type answer here

Correct Answer: -\frac{7}{2}

Deg^°

Rad

Math Response

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

STEP 3:

Evaluate the antiderivative at the lower limit.

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

Type answer here

Correct Answer: -\frac{7}{8}

Deg^°

Rad

Math Response

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

STEP 4:

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

Type answer here

Correct Answer: -\frac{21}{8}

Deg^°

Rad

Single answer

QUESTION 3:

Evaluate the definite integral.

(next slide)

Math Response

Evaluate the definite integral.

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

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

Type answer here

Correct Answer: 22.364

Deg^°

Rad

Multiple Steps

Math Response

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

STEP 1:

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

(no need to write down the +C)

Type answer here

Correct Answer: \frac{2x^{\frac{4}{3}}}{\frac{4}{3}}

Deg^°

Rad

Math Response

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

STEP 2:

Evaluate the antiderivative at the upper limit.

Type answer here

Correct Answer: 24

Deg^°

Rad

Math Response

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

STEP 3:

Evaluate the antiderivative at the lower limit.

Type answer here

Correct Answer: 0

Deg^°

Rad

Math Response

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

STEP 4:

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

Type answer here

Correct Answer: 24

Deg^°

Rad

Single answer

QUESTION 5:

Evaluate the definite integral.

(next slide)

Math Response

Evaluate the definite integral.

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

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

Type answer here

Correct Answer: 4.605

Deg^°

Rad

Multiple Steps

QUESTION 6:

Find the area of the shaded region.

(next slide)

Drag and Drop

STEP 1: Which's the operation for calculating the area?​ ​ ​

Placeholder

Drag these tiles and drop them in the correct blank above

Math Response

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

STEP 2:

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

(no need to write down the +C)

Type answer here

Correct Answer: -\frac{x^5}{5}+\frac{3x^4}{4}

Deg^°

Rad

Math Response

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

STEP 3:

Evaluate the antiderivative at the upper limit.

Type answer here

Correct Answer: 12.15

Deg^°

Rad

Math Response

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

STEP 4:

Evaluate the antiderivative at the lower limit.

Type answer here

Correct Answer: 0

Deg^°

Rad

Math Response

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

STEP 5:

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

Type answer here

Correct Answer: 12.15

Deg^°

Rad

Single answer

QUESTION 7:

Evaluate the definite integral.

(next slide)

Math Response

Evaluate the definite integral.

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

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

Type answer here

Correct Answer: 0

Deg^°

Rad

Well done !

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