1.9.27 Integration by substitution (reverse chain rule) (A-level only)

Given that $k\,$ is a positive constant,

a.

find

\int \frac{8x}{2x^2 + k} \, dx

[2]

b.

Given also that

\int_{1}^{4} \frac{8x}{2x^2 + k} \, dx = \ln 81

find the value of $k$ .

[5]

Given that $k\,$ is a positive constant,

a.

find

\int \frac{8x}{2x^2 + k} \, dx

[2]

b.

Given also that

\int_{1}^{4} \frac{8x}{2x^2 + k} \, dx = \ln 81

find the value of $k$ .

[5]

1.9.27 Integration by substitution (reverse chain rule) (A-level only) Questions