Using Properties of Definite Integrals Given ∫ − 1 1 f ( x ) d x = 0 and ∫ 0 1 f ( x ) d x = 5 , evaluate (a) ∫ − 1 0 f ( x ) d x . (b) ∫ 0 1 f ( x ) d x − ∫ − 1 0 f ( x ) d x . (c) ∫ − 1 1 3 f ( x ) d x . (d) ∫ 0 1 3 f ( x ) d x .
Using Properties of Definite Integrals Given ∫ − 1 1 f ( x ) d x = 0 and ∫ 0 1 f ( x ) d x = 5 , evaluate (a) ∫ − 1 0 f ( x ) d x . (b) ∫ 0 1 f ( x ) d x − ∫ − 1 0 f ( x ) d x . (c) ∫ − 1 1 3 f ( x ) d x . (d) ∫ 0 1 3 f ( x ) d x .
Solution Summary: The author explains how to calculate a definite integral using the provided values. The additive interval property is: if f(x) is integrable on the three closed intervals determined by
Using Properties of Definite Integrals Given
∫
−
1
1
f
(
x
)
d
x
=
0
and
∫
0
1
f
(
x
)
d
x
=
5
, evaluate
(a)
∫
−
1
0
f
(
x
)
d
x
.
(b)
∫
0
1
f
(
x
)
d
x
−
∫
−
1
0
f
(
x
)
d
x
.
(c)
∫
−
1
1
3
f
(
x
)
d
x
.
(d)
∫
0
1
3
f
(
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.
(3) Evaluate the definite integral
-3.5
(a) √25 √7-2xdx
(b) fote-t²/2dt.
Consider the indefinite integral ∫ (cos 2x)/(√sin 2x) dxdx.(a) Indicate the substitution u = u(x) you use and write the given integral as∫f(u) du.
(b) Evaluate the integral from part (a), and use this to evaluate the originalindefinite integral. Write the answer in terms of a function of x
If possible, evaluate the following definite integrals. If it is not possible, explain why not.
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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