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Let . Which of the following is…
MATHEMATICS · Single correct · CBSE · Mathematics · Integrals · Integrals
Problem
Let
F
(
x
)
=
∫
3
x
1
+
e
t
d
t
F(x)=\displaystyle\int_{3}^{x} \sqrt{1+e^{t}}\,dt
F
(
x
)
=
∫
3
x
1
+
e
t
d
t
. Which of the following is
F
′
(
x
)
F'(x)
F
′
(
x
)
? (a)
1
+
e
3
\sqrt{1+e^{3}}
1
+
e
3
(b)
e
x
1
+
e
x
e^{x}\sqrt{1+e^{x}}
e
x
1
+
e
x
(c)
1
+
e
x
\sqrt{1+e^{x}}
1
+
e
x
(d)
e
x
2
1
+
e
x
\displaystyle\dfrac{e^{x}}{2\sqrt{1+e^{x}}}
2
1
+
e
x
e
x
Related theory
Accumulation Concepts
Fundamental theorem of calculus
Integrals
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