Area Consider the three regions A , B . and C determined by the graph of f ( x ) = arcsin x , as shown in the figure. (a) Calculate the areas of regions A and B. (b) Use your answers in part (a) to evaluate the integral ∫ 1 / 2 2 / 2 arcsin x d x . (c) Use tlie methods in part (a) to evaluate the integral ∫ 1 3 ln x d x . (d) Use the methods in part (a) to evaluate the integral ∫ 1 3 arctan x d x .
Area Consider the three regions A , B . and C determined by the graph of f ( x ) = arcsin x , as shown in the figure. (a) Calculate the areas of regions A and B. (b) Use your answers in part (a) to evaluate the integral ∫ 1 / 2 2 / 2 arcsin x d x . (c) Use tlie methods in part (a) to evaluate the integral ∫ 1 3 ln x d x . (d) Use the methods in part (a) to evaluate the integral ∫ 1 3 arctan x d x .
Solution Summary: The author calculates the area of the regions A,B,C determined by the graph of f(x)=mathrmsin-1x.
Area Consider the three regions A, B. and C determined by the graph of
f
(
x
)
=
arcsin
x
, as shown in the figure.
(a) Calculate the areas of regions A and B.
(b) Use your answers in part (a) to evaluate the integral
∫
1
/
2
2
/
2
arcsin
x
d
x
.
(c) Use tlie methods in part (a) to evaluate the integral
∫
1
3
ln
x
d
x
.
(d) Use the methods in part (a) to evaluate the integral
∫
1
3
arctan
x
d
x
.
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