GATE CE 2026 Set 1 — Question 36
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Engineering Mathematics → Calculus → Definite & Indefinite Integrals
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Question
Let be a continuous function defined in and satisfying the equationThe value of is
Correct answer
(C) (1)/(2)
Solution
The given equation is . Rearranging, we get .Consider the integral of the perfect square :Substituting the known values:Since the integrand is non-negative and continuous, its integral being zero implies for all .
Thus, .
At , .
Thus, .
At , .
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