Find the upper area enclosed by \(f\left( x \right) = x\sqrt x \), \(x\)-axis and the vertical lines \(x = 0\) and \(x = 1\) using 4 intervals, correcting to four significant figures.

Area =

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Incorrect

Question 4 of 10

4. Question

Find the value of \(k\) if \(\int_2^k {\dfrac{3}{{{x^2}}}dx} = \dfrac{9}{{10}}\).

Correct

Incorrect

Question 5 of 10

5. Question

Find \(a\), if \(\int_{ – 1}^1 {{{\left( {\dfrac{{ – x + 1}}{2}} \right)}^5}} dx = \dfrac{a}{3}\).

\(a\)

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Incorrect

Question 6 of 10

6. Question

Find the area between the \(x\)-axis and \(y = x – 2\) from \(x = 1\) to \(x = 3\).

Area =

Correct

Incorrect

Question 7 of 10

7. Question

Find the area of the region bounded by \(y = {x^3} – 2x\) and \(y = 2x\), correcting to one decimal place.

Correct

Incorrect

Question 8 of 10

8. Question

A particle is initially at the origin, and is stationary. It accelerates according to \(a\left( t \right) = \dfrac{1}{{{{\left( {t + 1} \right)}^2}}}\) m/s^{2}. Find the best description of the motion of the particle at \(t = 3\).

Correct

Incorrect

Question 9 of 10

9. Question

Find the volume of the solid formed when \(y = {x^3} \) for \(0 \le x \le 2\) is revolved through \(2\pi \) or \(360^\circ \) about the \(y\)-axis. correcting to three significant figures.

Correct

Incorrect

Question 10 of 10

10. Question

If the area between the line \(y = {x^3}\) and the curve \(y = {x^2}\) is rotated about the \(x\)-axis, the volume is \(\dfrac{a}{b}\pi \). Find \(a\) and \(b\), where \(a\) and \(b\) have no common factors.