Mathematics, 14.01.2020 17:31 aprilreneeclaroxob0c

Determine whether the statement is true or false, and explain why.
integration by parts should be used to evaluate ∫^1_0 xe^10x dx.

Answers: 2

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Answers

Answer from: potato3999

True

General Formulas and Concepts:

Calculus

Differentiation

DerivativesDerivative Notation

Basic Power Rule:

f(x) = cxⁿf’(x) = c·nxⁿ⁻¹

Integration

Integrals

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

Integration by Parts: $\displaystyle \int {u} \, dv = uv - \int {v} \, du$

[IBP] LIPET: Logs, inverses, Polynomials, Exponentials, Trig

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle \int\limits^1_0 {xe^{10x}} \, dx$

Step 2: Integrate Pt. 1

Identify variables for integration by parts using LIPET.

Set u: $\displaystyle u = x$ [u] Basic Power Rule: $\displaystyle du = dx$ Set dv: $\displaystyle dv = e^{10x} \ dx$ [dv] Exponential Integration [U-Substitution]: $\displaystyle v = \frac{e^{10x}}{10}$

Step 3: integrate Pt. 2

[Integral] Integration by Parts: $\displaystyle \int\limits^1_0 {xe^{10x}} \, dx = \frac{xe^{10x}}{10} \bigg| \limits^1_0 - \int\limits^1_0 {\frac{e^{10x}}{10}} \, dx$ [Integral] Rewrite [Integration Property - Multiplied Constant]: $\displaystyle \int\limits^1_0 {xe^{10x}} \, dx = \frac{xe^{10x}}{10} \bigg| \limits^1_0 - \frac{1}{10} \int\limits^1_0 {e^{10x}} \, dx$ [Integral] Exponential Integration: $\displaystyle \int\limits^1_0 {xe^{10x}} \, dx = \frac{xe^{10x}}{10} \bigg| \limits^1_0 - \frac{1}{10} \bigg( \frac{e^{10x}}{10} \bigg) \bigg| \limits^1_0$ Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^1_0 {xe^{10x}} \, dx = \frac{9e^{10}}{100} + \frac{1}{10}$ Simplify: $\displaystyle \int\limits^1_0 {xe^{10x}} \, dx = \frac{9e^{10} + 1}{100}$

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

Unit: Integration

Answer from: joshblubaugh

True

Step-by-step explanation:

The integral

$\int\limits^1_0 {xe^{10x}} \, dx$

in the integral we have a product of a monomial:

and an exponential function: $e^{10x}$

In general case, when we have a combination of these two things you can use the integration by parts, where will be and $e^{10x}$ will be .

The statement is true

Answer from: Quest

i don't see any

step-by-step explanation:

Answer from: Quest

i think it would be c

mark brainliest if im right

step-by-step explanation:

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Determine whether the statement is true or false, and explain why.
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