Evaluate the following questions : ∫( + ) dt
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Answered by
1
Answer:
For the following indefinite integral, determine the corresponding function: \int \dfrac{1}{(9-x^2)^{3/2}} dx. View Answer · Evaluate the following definite ...
Answered by
0
Answer:
=∫
0
2
π
4+5cosx
1
dx
Substitute tan(
2
x
)=t⇒
2
1
sec
2
(
2
x
)dx=dt
So, x→0 ⇒t→0 and x→
2
π
⇒t→1
gives cosx=
1+t
2
1−t
2
,dx=
1+t
2
2dt
⇒ I=∫
0
1
4+5
1+t
2
1−t
2
1
1+t
2
2dt
=2∫
0
1
9−t
2
1
dt
⇒ I=
3
2
∫
0
1
1−
9
t
2
1
dt
Substitute
3
t
=u⇒dt=3du
So, t→0 ⇒u→0 and t→1 ⇒u→
3
1
⇒ I=
3
2
∫
0
3
1
1−u
21
du= 32 [ 21log 1−u1+u ] 031
⇒ I= 31 (log2−0) = 31 log2
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