Mathematics, 14.01.2020 22:31 lexie7752

Use integration by parts to derive the following formula from the table of integrals.
∫x^n . e^ax dx=x^ne^ax/a-n/a∫x^n-1e^ax dx +c, a≠-0.

Answers: 3

Show answers

Answers

Answer from: testedagent2823

See explanation.

General Formulas and Concepts:

Calculus

Differentiation

DerivativesDerivative Notation

Basic Power Rule:

f(x) = cxⁿf’(x) = c·nxⁿ⁻¹

Integration

Integrals[Indefinite Integrals] Integration Constant C

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

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:

*Note:

Treat a and n as arbitrary constants.

Step 1: Define

Identify

$\displaystyle \int {x^ne^{ax}} \, dx$

Step 2: Integrate Pt. 1

Identify variables for integration by parts using LIPET.

Set u: $\displaystyle u = x^n$ [u] Basic Power Rule: $\displaystyle du = nx^{n - 1} \ dx$ Set dv: $\displaystyle dv = e^{ax} \ dx$ [dv] Exponential Integration [U-Substitution]: $\displaystyle v = \frac{e^{ax}}{a}$

Step 3: Integrate Pt. 2

[Integral] Integration by Parts: $\displaystyle \int {x^ne^{ax}} \, dx = \frac{x^na^{ax}}{a} - \int {\frac{nx^{n - 1}e^{ax}}{a}} \, dx$ [Integral] Rewrite [Integration Property - Multiplied Constant]: $\displaystyle \int {x^ne^{ax}} \, dx = \frac{x^na^{ax}}{a} - \frac{n}{a} \int {x^{n - 1}e^{ax}} \, dx ,\ a \neq 0$

∴ We have verified/derived the formula.

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

Unit: Integration

Answer from: Quest

No a triangle cannot be formed because when you add the two smallest number together (which would be 11) the have to be bigger than the number it is "against" ( which would be 12)

Answer from: Quest

4 puzzles in 3 hours

step-by-step explanation:

Another question on Mathematics

Mathematics, 21.06.2019 17:00

What is the definition of exponential decay?

Answers: 3

Answer

Mathematics, 22.06.2019 02:30

Flvs question 3 exam: 04.10 segment one exam part two what is the measure of angle x? picture is shown

Answers: 1

Answer

Mathematics, 22.06.2019 02:50

Aci is desired for the true average stray-load loss μ (watts) for a certain type of induction motor when the line current is held at 10 amps for a speed of 1500 rpm. assume that stray-load loss is normally distributed with σ = 2.3. (round your answers to two decimal places.)

Answers: 1

Answer

Mathematics, 22.06.2019 03:30

Caitlin had 402. in her bank account.she withdrew $15.each week to pay for swimming lesson. she now has $237.

Answers: 1

Answer

You know the right answer?

Use integration by parts to derive the following formula from the table of integrals.
∫x^n . e...

Questions

Mathematics, 04.10.2020 17:01

PLEASE ANSWER FAST Point T is on line segment \overline{SU} SU . Given TU=x-1,TU=x−1, SU=3x-7,SU=3x−7, and ST=x+7,ST=x+7, determine the...