1.consider the integral , where n is a non-negative integer
\({I}_{n}= \int_{0}^{1} x^ne^{-2x} dx, \)
i)express \({I}_{n} \) in terms of f\({I}_{n-1} \)or n>=1.
ii) hence , evalutae \(\int_{1}^{e}(lny/y)^3\) dy
2. Given a constant a>0, show that \(\int_{-a}^{a} f(x)dx=\int_{0}^{a}[f(-x)+f(x)]dx \)
and hence, given that \(\int_{-1}^{1} ln(x+\sqrt{1+x^2}) dx\)
3. prove or disprove :If f is continuous , then \(\int_{0}^{1} f(x) dx= \int_{0}^{1} f(1-x)dx\) \(\)
