"Evaluate the given integral. ∫xcos⁡xdx" was answered by our community

pavitorj6

Answered question

2021-11-21

Evaluate the given integral.

\int x \cos x d x

pseudoenergy34

Beginner2021-11-22Added 22 answers

Step 1
To evaluate the given integral
Step 2
given integral is

\int x \cos x d x

applying integrating by parts

\int u v d x = u \int v d x - \int (\frac{d u}{d x} \int v d x) d x

let u=x and

v = \cos x

\int x \cos x d x = x \int \cos x d x - \int 1 \sin x d x

= x \sin x - \int \sin x d x

= x \sin x + \cos x + c

Cherry McCormick

Beginner2021-11-23Added 23 answers

Step 1: Use Integration by Parts on

\int x \cos x d x

.
Let u=x,

d v = \cos x, d u = d x, v = \sin x

Step 2: Substitute the above into

u v - \int v d u

x \sin x - \int \sin x d x

Step 3: Use Trigonometric Integration: the integral of

\sin x i s - \cos x

x \sin x + \cos x

Step 4: Add constant.

x \sin x + \cos x + C

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