Study Guide Ch.26. DEFINITE INTEGRALS

JEE Syllabus

definite integrals and their properties, application of the Fundamental Theorem of Integral Calculus.
Integration by parts, integration by the methods of substitution and partial fractions, application of definite integrals to the determination of areas involving simple curves.
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JEE question
If f″(x) = − f(x) and g(x) = f′(x) and F(x) = [f(x/2)]^2 + [g(x/2)]^2 and given that F(5) = 5 then F(10) is equal to

(A) 5
(B) 10
(C) 0
(D) 15

answer A
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