1.8.8 Integration by substitution (A-level only)

a.

Using the substitution $\sqrt{3x+1}$ , show that

\int_{1}^{5} \sqrt{12x+4} e^{\sqrt{3x+1}} \, dx

may be expressed in the form

\int_{a}^{b} k u^2 e^u \, du

where $a$ , $b$ and $k$ are constants to be found.

[4]

b.

Hence find, by algebraic integration, the exact value of

\int_{1}^{5} \sqrt{12x+4} e^{\sqrt{3x+1}} \, dx

giving your answer in simplest form.

[4]

a.

Using the substitution $\sqrt{3x+1}$ , show that

\int_{1}^{5} \sqrt{12x+4} e^{\sqrt{3x+1}} \, dx

may be expressed in the form

\int_{a}^{b} k u^2 e^u \, du

where $a$ , $b$ and $k$ are constants to be found.

[4]

b.

Hence find, by algebraic integration, the exact value of

\int_{1}^{5} \sqrt{12x+4} e^{\sqrt{3x+1}} \, dx

giving your answer in simplest form.

[4]

1.8.8 Integration by substitution (A-level only) Questions