Question

What is the area bounded by the curve y = x^2 – 5x + 4, x = 2, x = 3, x-axis in the following diagram?

(a) 13

(b) 6

(c) \(\frac{13}{6}\)

(d) \(\frac{6}{13}\)

I had been asked this question in an online quiz.

This question is from Quadrature topic in division Integral Calculus of Engineering Mathematics

Answer 1

The correct answer is (c) \(\frac{13}{6}\)

For explanation I would say: The area lies below the x-axis.

Area = ∫ -y dx

= \(\int_2^3 -(x^2-5x+4) dx\)

= \(\displaystyle\bigg[\frac{x^3}{3} – 5 \frac{x^2}{2} + 4x\bigg]_2^3\)

= \(-[(9 – (\frac{45}{2}) +12) – ((\frac{8}{3}) – (\frac{20}{2}) + 8)] \)

= \(– \left(-\frac{13}{6}\right)\)

= \(\frac{13}{6} \) sq.units.