Aspire Faculty ID #18348 · Topic: AMU MCA 2016 · Just now
AMU MCA 2016

The value of the integral $\int_{0}^{1} \frac{e^{5\log_e x} - e^{4\log_e x}}{e^{\log_e x^3} - e^{\log_e x^2}} , dx$ is

Solution

Use $e^{\log_e x^n} = x^n$ So integral becomes: $\int_{0}^{1} \frac{x^5 - x^4}{x^3 - x^2} , dx$ Factor: $= \int_{0}^{1} \frac{x^4(x-1)}{x^2(x-1)} , dx$ Cancel $(x-1)$: $= \int_{0}^{1} x^2 , dx$ $= \left[\frac{x^3}{3}\right]_0^1 = \frac{1}{3}$
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