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TIFR CSE 2019 | Part A | Question: 13

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Consider the integral

$$\int^{1}_{0} \frac{x^{300}}{1+x^2+x^3} dx$$

What is the value of this integral correct up to two decimal places?

  1. $0.00$
  2. $0.02$
  3. $0.10$
  4. $0.33$
  5. $1.00$
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$\displaystyle \int^{1}_{0} \frac{x^{300}}{1+x^2+x^3} dx \leq \int^{1}_{0} {x^{300}} dx (\because 1+x^2+x^3 \geq 1)$

$\qquad \qquad \leq \left[\frac{x^{301}}{301}\right]_0^1\leq \frac{1}{301} \leq  0.0033$

Only option matching is Option A.
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(a)  is answer.

We can prove this to be less than 0.009 and select option a.

https://drive.google.com/file/d/1Cr5cSe0nzq_RFruzPlVkTfGIDKPFFISz/view?usp=drivesdk

See this image in above link

 

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