Mathematics, 06.06.2020 17:00 jazzy4211

Evaluate the following Integrals ∫sin

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Answer from: chrisgramjooooo2366

$\displaystyle \int {xsinx} \, dx = -xcosx + sinx + C$

General Formulas and Concepts:

Calculus

Differentiation

DerivativesDerivative Notation

Basic Power Rule:

f(x) = cxⁿf’(x) = c·nxⁿ⁻¹

Integration

IntegralsIndefinite IntegralsIntegration Constant C

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

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

$\displaystyle \int {xsinx} \, dx$

Step 2: Integrate Pt. 1

Identify variables for integration by parts using LIPET.

Set u: $\displaystyle u = x$ [u] Differentiate [Basic Power Rule]: $\displaystyle du = dx$ [dv] Trigonometric Integration: $\displaystyle v = -cosx$ Set dv: $\displaystyle dv = sinx \ dx$

Step 3: Integrate Pt. 2

[Integral] Integration by Parts: $\displaystyle \int {xsinx} \, dx = -xcosx - \int {-cosx} \, dx$ [Integral] Rewrite [Integration Property - Multiplied Constant]: $\displaystyle \int {xsinx} \, dx = -xcosx + \int {cosx} \, dx$ [Integral] Trigonometric Integration: $\displaystyle \int {xsinx} \, dx = -xcosx + sinx + C$

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

Unit: Integration

Book: College Calculus 10e

Answer from: Quest

282 6/7 cm^2

step-by-step explanation:

Answer from: Quest

The correct answer is: b

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Evaluate the following Integrals ∫sin...

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