Class/Course - Engineering Entrance

Subject - Mathematics

Chapter - Integral Calculas

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Q.1 Let f(x) be a function satisfying f'(x) = f(x) with f(0) = 1 and g(x) be a function that satisfies f(x) g(x) = x2. Then the value of the integral $\int_{0}^{1} f\left (x \right ) g\left (x \right )dx$, is
  $e - \frac{e^{2}}{2} - \frac{5}{2}$
  $e\frac{e^{2}}{2} - \frac{3}{2}$
  $e - \frac{e^{2}}{2} - \frac{3}{2}$
  $e \frac{e^{2}}{2} \frac{5}{2}$