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

introduction, methodology, results, discussion

step-by-step explanation:

an observational study is one which consists of actual observation to record data and then analyse the data.

there are a number of factors that should be analyzed before starting an observational study.

the main four factors are:

i) introduction: this should be analysed to check whether the purpose of the study is correctly established and the data recorded are appropriate for the study

methodology: the method of collecting the data, such as whether randomly selected, and whether sample size matches with the population to be studied, whether questions asked are easy to answer by common men, etc.

results: then results such as summary of data with comments should be studied thoroughly

discussion: the last is the discussion, this can be either by management people or persons who are all interested , etc.

Answer from: Quest

The answers 5 so there’s the you need trust me it’s right

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