Question 1 Report
Evaluate: \(^9{?}_1\) \(\frac{x(2x-3)}{?x}\) dx
Simplify the integrand first. Since \(\sqrt{x}=x^{1/2}\):
\[\frac{x(2x-3)}{\sqrt{x}}=\frac{2x^{2}-3x}{x^{1/2}}=2x^{3/2}-3x^{1/2}\]
Integrate:
\[\int_{1}^{9}\left(2x^{3/2}-3x^{1/2}\right)dx=\left[\frac{4}{5}x^{5/2}-2x^{3/2}\right]_{1}^{9}\]
At \(x=9\): \(9^{5/2}=3^{5}=243\) and \(9^{3/2}=27\), giving \(\tfrac45(243)-2(27)=194.4-54=140.4\).
At \(x=1\): \(\tfrac45-2=-1.2\).
\[140.4-(-1.2)=141.6=\frac{708}{5}\]
Answer Details
The table shows the distribution of monthly income (in thousands of naira) of workers in a factory Monthly Income (N'1000) 135-139 140-149 150-154 155-164 16...
Given that (p + 1/2√3)(1 - √3)\(^2\) = 3- √3, find x the value of p.
Given that x = \(\begin{pmatrix} -4 \\ 3 \end{pmatrix}\) and y= \(\begin{pmatrix} -9 \\ 15 \end{pmatrix}\) calculate, correct to the nearest degree, the angl...
(a) A jogger is training for 15km charity race. He starts with a run of 500 metres, then he increases the distance he runs daily by 250 metres. (i) How many ...
A bag contains 24 mangoes out of which six are bad. If 6 mangoes are selected randomly from the bag with replacement, find the probability that not more than...
The polynomial f(x) =2x\(^3\) + px+ qx - 5 has (x-1) as a factor and a remainder of 27 when divided by (x + 2), where p and q are constants. Find the values ...
(a) The speed of a moving bus reduced from 45m/s to 5m/s with a uniform retardation of 10m/s\(^2\). Calculate the distance covered. (b) A bucket full of wate...
\(^{5y}{C}_2\) = 190, find the value of y
Everything you need to excel in your exams