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Byju's Answer
Standard XII
Mathematics
Second Fundamental Theorem of Calculus
Prove ∫0π/...
Question
Prove
∫
π
4
0
2
tan
3
x
d
x
=
1
−
log
2
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Solution
Let
I
=
∫
π
4
0
2
tan
3
x
d
x
I
=
2
∫
π
4
0
tan
2
x
tan
x
d
x
=
2
∫
π
4
0
(
sec
2
x
−
1
)
tan
x
d
x
=
2
∫
π
4
0
sec
2
x
tan
x
d
x
−
2
∫
π
4
0
tan
x
d
x
=
2
[
tan
2
x
2
]
π
4
0
+
2
[
log
cos
x
]
π
4
0
=
1
+
2
[
log
cos
π
4
−
log
cos
0
]
=
1
+
2
[
log
1
√
2
−
log
1
]
=
1
−
log
2
−
log
1
=
1
−
log
2
Hence, the given result is proved.
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Second Fundamental Theorem of Calculus
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