Matched Problem 3 Referring to the figure for Example 3, calculate the definite integral (A) ∫ a 0 f ( x ) d x (B) ∫ 0 c f ( x ) d x (C) ∫ 0 b f ( x ) d x EXAMPLE 3 Definite Integrals Calculate the definite integrals by referring to Figure 9. (A) ∫ a b f ( x ) d x (B) ∫ a c f ( x ) d x (C) ∫ b c f ( x ) d x
Matched Problem 3 Referring to the figure for Example 3, calculate the definite integral (A) ∫ a 0 f ( x ) d x (B) ∫ 0 c f ( x ) d x (C) ∫ 0 b f ( x ) d x EXAMPLE 3 Definite Integrals Calculate the definite integrals by referring to Figure 9. (A) ∫ a b f ( x ) d x (B) ∫ a c f ( x ) d x (C) ∫ b c f ( x ) d x
Solution Summary: The above integral indicates the sum of area of the region A, from a to 0. The regions A lies in third quadrant with its area 2.33.
Matched Problem 3 Referring to the figure for Example 3, calculate the definite integral
(A)
∫
a
0
f
(
x
)
d
x
(B)
∫
0
c
f
(
x
)
d
x
(C)
∫
0
b
f
(
x
)
d
x
EXAMPLE 3 Definite Integrals Calculate the definite integrals by referring to Figure 9.
(A)
∫
a
b
f
(
x
)
d
x
(B)
∫
a
c
f
(
x
)
d
x
(C)
∫
b
c
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.
According to Newton's law of universal gravitation, the force F between two bodies of constant mass
GmM
m and M is given by the formula F =
, where G is the gravitational constant and d is the
d²
distance between the bodies.
a. Suppose that G, m, and M are constants. Find the rate of change of force F with respect to
distance d.
F' (d)
2GmM
b. Find the rate of change of force F with gravitational constant G = 6.67 × 10-¹¹ Nm²/kg², on
two bodies 5 meters apart, each with a mass of 250 kilograms. Answer in scientific notation,
rounding to 2 decimal places.
-6.67x10
N/m syntax incomplete.
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