CUET PG 2023 Mathematics PYQ — Given below are two statements: Statement I: Statement II: is les… | Mathem Solvex | Mathem Solvex
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CUET PG 2023 — Mathematics PYQ
CUET PG | Mathematics | 2023
Given below are two statements: Statement I: ∫−aaf(x)dx=∫0a[f(x)+f(−x)]dx Statement II: ∫01(1+x)(1+x3)dx is less than or equal to 815 In the light of the above statements, choose the most appropriate answer from the options given below:
Choose the correct answer:
A.
Both Statement I and Statement II are correct
(Correct Answer)
B.
Both Statement I and Statement II are incorrect
C.
Statement I is correct but Statement II is incorrect
D.
Statement I is incorrect but Statement II is correct
Correct Answer:
Both Statement I and Statement II are correct
Explanation
Analysis of Statement I
Statement I is a standard property of definite integrals. Let's break the integral ∫−aaf(x)dx into two parts:
∫−aaf(x)dx=∫−a0f(x)dx+∫0af(x)dx
For the first integral ∫−a0f(x)dx, let's use the substitution x=−t, which implies dx=−dt.
