Mathematics, 20.09.2020 14:01 Katmcfee7681

Evaluate the definite integral.
1 x4(1 + 2x5)5 dx.

Answers: 2

Show answers

Answers

Answer from: tilly40oooo

$\displaystyle \int\limits^5_1 {x^4(1 + 2x^5)} \, dx = \frac{9768748}{5}$

General Formulas and Concepts:

Calculus

Differentiation

DerivativesDerivative Notation

Derivative Property [Multiplied Constant]: $\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)$

Derivative Property [Addition/Subtraction]: $\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)]$

Basic Power Rule:

f(x) = cxⁿf’(x) = c·nxⁿ⁻¹

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]: $\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)$

Integration Property [Multiplied Constant]: $\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx$

U-Substitution

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle \int\limits^5_1 {x^4(1 + 2x^5)} \, dx$

Step 2: Integrate Pt. 1

Identify variables for u-substitution.

Set u: $\displaystyle u = 1 + 2x^5$ [u] Differentiate [Basic Power Rule, Derivative Properties]: $\displaystyle du = 10x^4 \ dx$ [Bounds] Switch: $\displaystyle \left \{ {{x = 5,\ u = 1 + 2(5)^5 = 6251} \atop {x=1,\ u = 1 + 2(1)^5 = 3}} \right.$

Step 3: Integrate Pt. 2

[Integral] Rewrite [Integration Property - Multiplied Constant]: $\displaystyle \int\limits^5_1 {x^4(1 + 2x^5)} \, dx = \frac{1}{10}\int\limits^5_1 {10x^4(1 + 2x^5)} \, dx$ [Integral] U-Substitution: $\displaystyle \int\limits^5_1 {x^4(1 + 2x^5)} \, dx = \frac{1}{10}\int\limits^{6251}_3 {u} \, du$ [Integral] Reverse Power Rule: $\displaystyle \int\limits^5_1 {x^4(1 + 2x^5)} \, dx = \frac{1}{10} \bigg( \frac{u^2}{2} \bigg) \bigg| \limits^{6251}_3$ Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^5_1 {x^4(1 + 2x^5)} \, dx = \frac{1}{10}(19537496)$ Simplify: $\displaystyle \int\limits^5_1 {x^4(1 + 2x^5)} \, dx = \frac{9768748}{5}$

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

Unit: Integration

Answer from: Quest

it is a reproduction.

step-by-step explanation:

Select answer from the top-down menu to correctly complete the statementsa scale factor would it be

Answer from: Quest

can i get the link to the assignment?

step-by-step explanation:

Another question on Mathematics

Mathematics, 21.06.2019 19:00

Which expression converts 45 degree to radians

Answers: 2

Answer

Mathematics, 21.06.2019 22:00

Find two numbers if their sum is 91 and the ratio is 6: 7?

Answers: 1

Answer

Mathematics, 21.06.2019 22:00

Onnie is considering doing some long term investing with money that she inherited. she would like to have $50,000 at the end of 30 years. approximately how much money would lonnie need to put into an account earning 6% interest compounded annually in order to meet her goal?

Answers: 1

Answer

Mathematics, 22.06.2019 00:30

Francisco's credit card has an apr of 28.98%, calculated on the previous monthly balance. his credit card record for the last 7 months is shown in the table below francisco is trying to figure out what this all means. answer the following questions: what is the total amount that francisco has paid in interest over the 7 months? what is the total amount that francisco has made in payments over the 7 months? how much of francisco's payments have gone to paying down the principal on his account? what is francisco's new balance at the end of month 8? what will francisco be charged for interest for month 8?

Answers: 2

Answer

You know the right answer?

Evaluate the definite integral.
1 x4(1 + 2x5)5 dx....

Questions