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.
Let I =
f(x) dx, where f is the function whose graph is shown.
4
2
y
f
X
1
2
3
4
(a) Use the graph to find L2, R2 and M2.
R₂
M2
=
=
=
(b) Are these underestimates or overestimates of I?
O 42 is an underestimate.
O 42 is an overestimate.
◇ R2 is an underestimate.
OR2 is an overestimate.
OM2 is an underestimate.
○ M2 is an overestimate.
(c) Use the graph to find T2.
T₂ =
Vector u has a magnitude of 23 and vector v has a magnitude of 83. The angle between the two vectors is 126 degrees.a) Draw a fully-labelled vector diagram showing the two vectors and the resultant vector when they are added together.b) Find the magnitude of the resultant vector.c) Find the direction of the resultant vector relative to vector u.
Solding by finding the x and y of the vectors and adding
Find the range and all the answers. Remark that the range isn’t between -(pi/2) and (pi/2)
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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