Question

Intergral with boundaries pi and zero
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Answer 1

Hey there!

Kindly refer the following attachment for the detailed solution and explanations for the given integral boundary for yhe trigonometric function of sin, Final answer will be,

$\boxed{\bf{\underline{\int_0^{\pi} \: sin(x) \: dx = 2}}}$

Which is the required solution for this type of query.

Hope this helps you and solves your doubts for integration of boundaries!!!!

Answer 2

Suppose f(x)f(x) is a continuous function on [a,b][a,b] and also suppose that F(x)F(x) is any anti-derivative for f(x)f(x). Then,
∫baf(x)dx=F(x)|ba=F(b)−F(a)

Much easier than using the definitionwasn’t it? Let’s now use the second anti-derivative to evaluate this definite integral.
∫20x2+1dx=(13x3+x−1831)∣∣∣20=13(2)3+2−1831−(13(0)3+0−1831)=143−1831+1831=143


HOPE IT HELPED
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