MHT CET · Maths · Definite Integration
\(\int_0^2|2 x| \mathrm{d}=\) (where [.] denotes the greatest integer function.)
- A 4
- B 3
- C 2
- D 5
Answer & Solution
Correct Answer
(B) 3
Step-by-step Solution
Detailed explanation
\(\int_0^2[2 x] \mathrm{d} x=\int_0^{1 / 2} 0 \mathrm{~d} x+\int_{\frac{1}{2}}^1 1 \cdot \mathrm{d} x+\int_1^{3 / 2} 2 \mathrm{~d} x~+\) \(\int_{\frac{3}{2}}^2 3 \mathrm{~d} x \)
\( =0+\left(1-\frac{1}{2}\right)+2\left(\frac{3}{2}-1\right)+3\left(2-\frac{3}{2}\right) \)
\( =0+\frac{1}{2}+2 \times \frac{1}{2}+3 \times \frac{1}{2}=3\)
\( =0+\left(1-\frac{1}{2}\right)+2\left(\frac{3}{2}-1\right)+3\left(2-\frac{3}{2}\right) \)
\( =0+\frac{1}{2}+2 \times \frac{1}{2}+3 \times \frac{1}{2}=3\)
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