Evaluate the integral: _1^∞ 4/x^4 dx - Mathematics MCQ Mathematics Mock Test - 1 2026 | ExamTest.live

mediumMCQMathematics Mock Test - 12026Mathematics

11 attempts9% success rate1 mark

Evaluate the integral: \int_{1}^{\infty} \frac{4}{x ^{4}} d x

Solution & Step-by-step Explanation

Let I = \int_{1}^{\infty} \frac{4}{x ^{4}} d x .Using the rule \int x^{n} d x = \frac{x ^{n + 1}}{n + 1} : I = \int_{1}^{\infty} 4 x^{- 4} d x I = [4 \cdot \frac{x ^{- 3}}{- 3}]_{1}^{\infty} I = - \frac{4}{3} [\frac{1}{x ^{3}}]_{1}^{\infty} Applying limits: I = - \frac{4}{3} [\frac{1}{\infty ^{3}} - \frac{1}{1 ^{3}}] I = - \frac{4}{3} [0 - 1] I = \frac{4}{3}

Try it yourself before checking the explanation above.

Evaluate the integral: \int_{1}^{\infty} \frac{4}{x ^{4}} d x

\frac{2}{3}

\frac{4}{3}

\frac{1}{3}

None of the above

Practice with timed mock tests and track your performance across Mathematics.