3.6
1.
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(c) Let
. Then
and
.Now express the integrand interms ot
and
. Then
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(d) Let
. Then
. To find
, rewrite the above equation in
and solve for
.
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2.
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(b) Let
. Then
implies
. Now consider the traiangle with the angle
and whose opposite side is
and whose hypotenuse is 2. Then the bottom is
.Now let
. Then
and
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(d) Let
. Then
and
. Now consider the triangle with the angle
and whose opposite side is
and thee hypotenuse is 1. Then the bottom is
. Now
implies
and ,
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Let
. Then
and
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(e) Let
と. Then
and
. Now consider the triangle with the angle
and whose hypotenuse is
and the bottom is
. Then we have the opposite side is
.Then
implies
and
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(f) Let
. Then
and
. Consider the triangle with the angle
and whose opposite side is
and the bottom is 2. Then the hypotenuse is
.Now
and
.Also, ,
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(i) Completing the square, we have
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Now integrate
.
In this case, the degree of the numerator and the denominator is even. So, we let
. Then
and
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Therefore,
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