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Mathematics
01.10.2022 09:13
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What is the definite integral of #x^3# from 1 to 2?

What is the definite integral of #x^3# from 1 to 2?
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jstamey757
jstamey757
4,7(74 marks)

\displaystyle \int\limits^2_1 {x^3} \, dx = \frac{15}{4}

General Formulas and Concepts:

Calculus

Integration

Integrals

Integration Rule [Reverse Power Rule]:                                                               \displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C

Integration Rule [Fundamental Theorem of Calculus 1]:                                     \displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)

Step-by-step explanation:

Step 1: Define

Identify

\displaystyle \int\limits^2_1 {x^3} \, dx

Step 2: Integrate

[Integral] Reverse Power Rule:                                                                    \displaystyle \int\limits^2_1 {x^3} \, dx = \frac{x^4}{4} \bigg| \limits^2_1Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]:          \displaystyle \int\limits^2_1 {x^3} \, dx = \frac{15}{4}

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

sarahhope55
sarahhope55
5,0(69 marks)

1536

Step-by-step explanation:

If he drives 48 miles everyday for 32 days, to get his total you multiply to by 32

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