Question

If f(x) =$\sqrt{x}$, g(x) = e^x –1, &̣fog (x) dx =A fog (x) + B tan^–1(fog (x)) + C, then A + B is equal to

• A. 1
• B. 2
• C. 3
• D. None of these

Answer 1

Answer: (D)

None of these

Answer 2

fog (x) = $\sqrt{e^{x} - 1}$

\ I = $\int_{}^{}\sqrt{e^{x} - 1}$dx = $\int_{}^{}\frac{2t^{2}}{t^{2} + 1}$dt

{where $\sqrt{e^{x} - 1}$ = t }

= 2t–2 tan^–1 t + C = 2$\sqrt{e^{x} - 1}$–2 tan^–1 $(\sqrt{e^{x} - 1})$ + C

= 2 fog (x) – 2 tan^–1 (fog (x)) + C

\ A + B = 2 + (– 2) = 0