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Calculus Level 4

$\large \int_{0}^{1} \dfrac{x^{300}}{1 + x^2 + x^3} dx$

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

1.00 0.33 0.00 0.02 0.10

2 solutions

Mark Hennings
May 8, 2019

Without performing the integral, we note that $0 \; < \; \int_0^1 \frac{x^{300}}{x^3 + x^2 + 1}\,dx \; < \; \int_0^1 x^{300}\,dx \; = \; \tfrac{1}{301} \; < \; 5 \times 10^{-3}$ so, so $2$ decimal places, the nearest approximation is $\boxed{0.00}$ .

Kyle T
May 7, 2019

wolfram tells us the value is 0.00111357, correct up to 2 decimal places would be "0.00"

very nice solution thanks so helpful

Charley Shi - 2 years, 1 month ago

Pick up your pen

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