please help Evaluate the following integral using the Fundamental Theorem of Cal
ID: 2827971 • Letter: P
Question
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Evaluate the following integral using the Fundamental Theorem of Calculus. Discuss whether your result is consistent with the figure. (x2 - 2x + 8)dx (x2 - 2x + 8)dx = (Simplify your answer.) Evaluate the integral (sinx - cosx)dx using the fundamental theorem of calculus. Discuss whether your result is consistent with the figure shown to the right. (sinx - cosx)dx = Evaluate the following integral using the fundamental theorem of calculus. Sketch the graph of the integrand and shade the region whose net area you have found. (x2 + 3x - 10) dx (x2 + 3x - 10) dx =Explanation / Answer
1.) On integrating we get
x^3/3 - x^2 + 8x from x = 0 to 1
on plug in limits,
1/3 - 1 + 8 - 0
= 7+ 1/3 = 22/3
2.) on integrating,
(-cos x + sin x) from x = - pi/4 to x = 7pi/4
on plug in limits,
- cos 7 pi/4 + sin 7pi/4 + cos pi/4 + sin pi/4
= - 1/sqrt 2 - 1/ sqrt 2 + 1/ sqrt 2 + 1/sqrt 2
=0
3.) on integrating,
x^3/3 + 3x^2/2 - 10x
On plug in limits,
8/3 + 6 - 20 + 125/3 - 125/2 -50
= -343/6
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