IB Maths AA SL AA 5.3 Integration questions

Exam-style questions in the shape of Paper 1 and Paper 2, with full markschemes. Read the markscheme, or type, photograph or draw your answer and get it marked.

Question 1

Paper 1, no calculatorEasy5 marks

The derivative of a function ff is

f′(x)=6x+2,x∈R,f'(x)=6x+2,\qquad x\in\mathbb{R},

and f(0)=3f(0)=3

(a)

Determine f(x)f(x)

[4]
(b)

Hence write down a definite integral representing the area bounded by the graph y=f(x)y=f(x) the xx-axis, x=0x=0 and x=2x=2 Do not evaluate the integral.

[1]

Question 2

Paper 1, no calculatorEasy7 marks

The curve y=x2−1y=x^2-1 the xx-axis and the lines x=−2x=-2 and x=2x=2 bound several regions.

(a)

Write down, without evaluating, an expression in terms of definite integrals for the total area of these regions.

[3]
(b)

Hence determine the exact total area of these regions.

[4]

The best questions are still waiting

Unlock every question in this topic, then type, photograph or draw your answer and have it marked against the markscheme. Find out where you are dropping marks.