Integrating exponentials and trigonometric functionsAQA A-Level Maths: Mind map

Exam questions on Integrating exponentials and trigonometric functions

1. A curve has gradient function $\frac{dy}{dx}=6e^{3x}$ and passes through the point $(0,5)$.
   Find the exact value of $\int_0^{\ln 2}6e^{3x}\,dx$.2 marks
2. A particle moves on a straight line. At time $t$ seconds its velocity is $v=4\cos 2t$ m s$^{-1}$, where $2t$ is in radians. The particle starts at the origin, so its displacement is $s=0$ when $t=0$.
   Find the total distance travelled by the particle between $t=0$ and $t=\frac{\pi}{2}$.2 marks
3. Let $f(x)=\frac{3}{x}-4e^{-2x}+5\cos\frac{x}{2}$ and $h(x)=\frac{3}{x}+5\cos\frac{x}{2}$, for $x>0$, where angles are in radians.
   Find $\int f(x)\,dx$.3 marks