IB Maths AA SL 5.5 Integration As Anti Differentiation Questions

Practise IB Mathematics SL 5.5 by applying integration as anti-differentiation methods to questions from the Question Bank.

Exam points

Integrate polynomial-type functions as anti-derivatives and verify the result by differentiation.
Use boundary conditions to determine constants, then connect anti-derivatives with definite integrals and area under a curve over stated limits.

[Maximum number: 3]

Find h(x).

recognition that $h(x)=\int h^{\prime}(x)$

\begin{aligned} & h(x)=\frac{1}{4} \mathrm{e}^{4 x}+6 x+c \\ & (h(1.5)=) \frac{1}{4} \mathrm{e}^{4(1.5)}+6(1.5)+c=105 \\ & c=-4.85719 \ldots \\ & h(x)=\frac{1}{4} \mathrm{e}^{4 x}+6 x-4.86\left(=\frac{1}{4} \mathrm{e}^{4 x}+6 x+96-\frac{1}{4} \mathrm{e}^{6}\right) \end{aligned}

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