Quick! What's its antiderivative?

Calculus Level 2

$\large \int_{2y}^{y^2} x^{x^{x^x}} e \cdot \ln | 9 | \ dx$

Find the value of the integral above if $\displaystyle y = \lim_{n \to \infty} \frac {6n-2}{3n+3}$ .

\ln(9)

1

0

e

-2

2

1 solution

Deepak Kumar
Apr 11, 2015

Upon solving the limit like (6-2/n)/(3+3/n)=> y=2 => y^2=2y => lower limit of integral=upper limit of integral and hence value becomes 0

Moderator note:

Correct. One common mistake students make is to first find its antiderivative which couldn't be found. Note that not all functions have antiderivatives that can be stated in terms of elementary functions. For example: $\int x^x dx, \int x \tan x dx, \int \sin(x^2) dx$ .

Did it the same way:)

Athiyaman Nallathambi - 5 years, 10 months ago

Quick! What's its antiderivative?

1 solution

Moderator note:

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