# CIE A level -Pure Mathematics 2 : Topic : 2.3 Trigonometry- properties and graphs of all six trigonometric functions : Exam Style Questions Paper 2

Question

(a) Find

(i)$$\int \frac{e^{2x}+6}{e^{2x}}$$,

(ii) $$\int 3\cos ^{2}xdx$$,

(b) Use the trapezium rule with 2 intervals to estimate the value of,

$$\int _{1}^{2}\frac{6}{\ln (x+2)}dx$$,

(a) (i) Attempt to divide by $$e^{2x}$$ and attempt to integrate 2 terms

Integrate a term of form $$ke^{-2x}$$ correctly.

Fully correct integral $$x-3e^{-2x}$$.

(ii) State correct expression $$\frac{1}{2}\cos 2x+\frac{1}{2}$$ or equivalent
Integrate an expression of the form a + b cos 2x, where ab ≠ 0, correctly
State correct integral $$\frac{3\sin 2x}{4}+\frac{3x}{2}$$.

(b) State or imply correct ordinates 5.46143…, 4.78941…, 4.32808…
Use correct formula, or equivalent, correctly with h = 0.5 and three ordinates
Obtain answer 4.84 with no errors seen