Question
Download Solution PDFComprehension
निर्देश : निम्नलिखित प्रश्नों के लिए नीचे दिए गए कथनों पर विचार करें:
माना f(x) = |x2 - x - 2|
\(\rm \int_1^3f(x)dx\) किसके बराबर है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFव्याख्या:
दिया गया है:
f(x) =|x2 - x - 2|
= {x2- x - 2; x ∈ (-∞, -1) ∪ (2, ∞)
- (x2 -x -2 ; x ∈[ -1,2]
माना I = \(\int_1^3f(x)dx\)
= \(- \int_1^2(x^2 -x-2)dx+ \int_2^3(x^2-x-2)dx\)
= \(- [\frac{x^3}{3} -\frac{x^2}{2}-2x]^2_1 + [\frac{x^3}{3} -\frac{x^2}{2}-2x]^3_2\)
= \([\frac{8}{3}-\frac{4}{2}-4] - [[\frac{1}{3}-\frac{1}{2}-2] + [\frac{27}{3}-\frac{9}{2}-6] - [\frac{8}{3}-\frac{4}{2}-4] \)
= \(\frac{20}{6} - \frac{13}{6} -\frac{9}{6} +\frac{20}{6}\) = 3
इसलिए, विकल्प (b) सही है।
Last updated on May 30, 2025
->UPSC has released UPSC NDA 2 Notification on 28th May 2025 announcing the NDA 2 vacancies.
-> A total of 406 vacancies have been announced for NDA 2 Exam 2025.
->The NDA exam date 2025 has been announced for cycle 2. The written examination will be held on 14th September 2025.
-> Earlier, the UPSC NDA 1 Exam Result has been released on the official website.
-> The selection process for the NDA exam includes a Written Exam and SSB Interview.
-> Candidates who get successful selection under UPSC NDA will get a salary range between Rs. 15,600 to Rs. 39,100.
-> Candidates must go through the NDA previous year question paper. Attempting the NDA mock test is also essential.