Dark mode

Further integration — Question 368

Original QCE Vault practice · 5 marks

Q368 · Practice questionTechnology-freeSimple familiar5 marks

QUESTION 368 (5 marks)

The curve is

y=x^2+1

for

0\leq x\leq2

.

Graph of x squared plus 1 on [0,2], with faint vertical boundaries for two unit-width strips.

a)

Use two equal strips to determine the left-endpoint and right-endpoint rectangle estimates.

[2 marks]

b)

Use integration to determine the exact area.

[2 marks]

c)

Explain why the two rectangle estimates bound the exact area.

[1 mark]

Question linkSyllabus coverage

Related questions

Q6 · Original practice · 1 mark
Evaluate $\displaystyle\int_0^2 3x^2\,dx$ .
Further integration
Q16 · Original practice · 1 mark
An antiderivative of $\dfrac{2x}{x^2+5}$ is
Further integration
Q31 · Original practice · 3 marks
Evaluate $\displaystyle\int_0^1\frac{4x}{x^2+1}\,dx$ .
Further integration
Q41 · Original practice · 3 marks
For $0\le x\le1$ , the graph $y=kx(1-x)$ lies above the $x$ -axis. The area between the graph and the $x$ -axis is 2 square units. Determine $k$ .
Further integration