MHT CET · Maths · Definite Integration

\(\int_{-2}^2\left|x^2-x-2\right| \mathrm{dx}=\)

A \(\frac{17}{3}\)
B \(\frac{19}{3}\)
C \(19\)
D \(17\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{19}{3}\)

Step-by-step Solution

Detailed explanation

Roots of \(x^2-x-2=0\) are \(x=-1, 2\). \(\int_{-2}^2\left(x^2-x-2\right) \mathrm{dx} = \int_{-2}^{-1}(x^2-x-2) \mathrm{dx} + \int_{-1}^{2}(-x^2+x+2) \mathrm{dx}\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

Explore more questions on app

From MHT CET

Match the mineral deficiency disorders given in Column I with their symptoms given in Column II.

Column I		Column II
i.	Chlorosis	a.	Localised death of tissues in leaves
ii.	Necrosis	b.	Premature fall of flowers, fruits and leaves
iii.	Mottling	c.	Yellowing of leaves due to absence of chlorophyll
iv.	Abscission	d.	Appearance of green and non- green patches on leaves

Choose the correct option from below.

MHT CET 2024 Hard

Explore more questions on app