Properties of integrals Suppose that ∫ 1 4 f ( x ) d x = 6 , and ∫ 1 4 g ( x ) d x = 4 , and ∫ 3 4 f ( x ) d x = 2 . Evaluate the following integrals or state that there is not enough information. 41. ∫ 1 4 ( 3 f ( x ) − 2 g ( x ) ) d x
Properties of integrals Suppose that ∫ 1 4 f ( x ) d x = 6 , and ∫ 1 4 g ( x ) d x = 4 , and ∫ 3 4 f ( x ) d x = 2 . Evaluate the following integrals or state that there is not enough information. 41. ∫ 1 4 ( 3 f ( x ) − 2 g ( x ) ) d x
Solution Summary: The author evaluates the value of integral displaystyle 'underset' 1overset4int by applying the appropriate properties and the fact.
Properties of integralsSuppose that
∫
1
4
f
(
x
)
d
x
=
6
, and
∫
1
4
g
(
x
)
d
x
=
4
, and
∫
3
4
f
(
x
)
d
x
=
2
. Evaluate the following integrals or state that there is not enough information.
41.
∫
1
4
(
3
f
(
x
)
−
2
g
(
x
)
)
d
x
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.
a. Explain why
0 ≤ x²arctan(x) ≤ (pi*x²)/4 for all 0 ≤ x ≤ 1.
b. Use the properties of the integrals to show that the value of the integral
lower bound is 0, higher bound is 1 and the integral is x² arctan(x) dx
lies on the interval [0,pi/12]
1) again consider the definite integral
2) consider the integral use either of the two methods of substitution
a.)If f '(x) = x7,what is f(x)? (Use C for the constant of integration.) f(x) =
b.)Evaluate the integral. Check your answer by differentiating. (Use C for the constant of integration.)
(x3 − 6x2 + 6) dx
Chapter 5 Solutions
MyLab Math with Pearson eText -- Standalone Access Card -- for Calculus: Early Transcendentals (3rd Edition)
Thomas' Calculus: Early Transcendentals (14th Edition)
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Numerical Integration Introduction l Trapezoidal Rule Simpson's 1/3 Rule l Simpson's 3/8 l GATE 2021; Author: GATE Lectures by Dishank;https://www.youtube.com/watch?v=zadUB3NwFtQ;License: Standard YouTube License, CC-BY