The area (in sq. units) of the region bounded by the curve \(y = x^{2}+x\), the x-axis and the lines x = 2 and x = 5 is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(\displaystyle\frac{99}{2}\)
For \(2 \le x \le 5\), \(x^{2}+x\) is positive, so the curve is above the x-axis and the area is the integral of y:
\( \displaystyle A = \int_{2}^{5} (x^{2}+x)\,dx \)
\( \displaystyle = \left[\frac{x^{3}}{3}+\frac{x^{2}}{2}\right]_{2}^{5} \)
\( \displaystyle = \frac{125-8}{3}+\frac{25-4}{2} \)
\( \displaystyle = 39+\frac{21}{2} = \frac{99}{2} \)