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Answer the following questions about the exponential function given below.
MATHEMATICS · Multi-part · CBSE · Mathematics · Integrals · Integrals
Problem
Answer the following questions about the exponential function given below. (i) Find the indefinite integral
∫
e
(
x
4
−
2
)
d
x
\displaystyle \int e^{\left(\frac{x}{4}-2\right)}\,dx
∫
e
(
4
x
−
2
)
d
x
. (ii) Using the antiderivative obtained in part (i), evaluate
∫
0
4
e
(
x
4
−
2
)
d
x
\displaystyle \int_{0}^{4} e^{\left(\frac{x}{4}-2\right)}\,dx
∫
0
4
e
(
4
x
−
2
)
d
x
. Leave your answer in simplest exact form.
Related theory
Advanced Differentiation
Antiderivatives
Standard algebraic integrals
Integration as inverse process of differentiation
Integrals
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