(Question 57 and 61 only) Definite integrals. Evaluate the following integrals using the fundamental theorem of calculus. 57.58.59.√3/²60.61.√362.11+x²sec x(sec x + cos x) dxz² +4Z-dxdxdz√√2 x√x² - 1[ f(x) da, where f(x)=3g(x) dx, where g(x)=sin x + 12 cos x + 2(3x² + 4x + 12x + 5if x ≤ π/2if x > π/2if x < 2if x > 2 57.59.061.63.П123+ 4 In 22Зп2- 1

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Answered: √3 1 -S₁² 1 + 22²²=² dx 1 57.

Math

Calculus

√3 1 -S₁² 1 + 22²²=² dx 1 57.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter4: Calculating The Derivative

Section4.5: Derivatives Of Logarithmic Functions

Problem 47E

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Question

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(Question 57 and 61 only) Definite integrals. Evaluate the following integrals using the fundamental theorem of calculus.

57.
58.
59.
√3/²
60.
61.
√3
62.
1
1+x²
sec x(sec x + cos x) dx
z² +4
Z
-dx
dx
dz
√√2 x√x² - 1
[ f(x) da, where f(x)
=
3
g(x) dx, where g(x)
=
sin x + 1
2 cos x + 2
(3x² + 4x + 1
2x + 5
if x ≤ π/2
if x > π/2
if x < 2
if x > 2

57.
59.0
61.
63.
П
12
3
+ 4 In 2
2
Зп
2
- 1

With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.

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