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

f(x) = y

f(-3) = -5

step-by-step explanation:

Answer from: Quest

option a is correct.

$\frac{\text{original height}}{\text{original base}}=\frac{\text{reduction height}}{\text{reduction base}}$

step-by-step explanation:

scale factor: it is used to find proportional measurements.

proportions means having the same ratio.

scale factor is the ratio of the model measurement to the actual measurement in a simplest form.

or we can say that the ratio of any two corresponding lengths in two similar geometric figures

if the scale factor is more than 1, then it is an enlargement,

if the scale factor less than 1, then it is a reduction.

given the two geometric figure:

by definition of proportions, we have

$\frac{\text{original height}}{\text{original base}}=\frac{\text{reduction height}}{\text{reduction base}}$

Which is the scale factor proportion for the reduction shown? answers are on picture.

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Evaluate the following Integrals ∫sin...