Easy Integration (Part a)

Calculus Level 1

Evaluate:

∫ 0 π sin ⁡ ( x ) d x \large \int_0^\pi \sin(x) dx


The answer is 2.

Sharky Kesa by Sharky Kesa , 19, United Kingdom

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2 solutions

L N
Jun 6, 2014

The integral of s i n ( x ) sin(x) is − c o s ( x ) -cos(x) hence, we want to evaluate: − c o s ( π ) − − cos ⁡ ( 0 ) -cos(\pi) - -\cos(0) which simplifies to: 1 − ( − 1 ) 1 - (-1) which simplifies to 1 + 1 1 + 1 2 \space 2

2 Helpful 0 Interesting 0 Brilliant 0 Confused

∫ 0 π sin ⁡ x d x = − cos ⁡ x ∣ 0 π = − ( − 1 ) + 1 = 2 \begin{aligned} \int_0^\pi \sin x \ dx & = - \cos x \ \bigg|_0^\pi = - (-1) + 1 = \boxed{2} \end{aligned}

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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