defence exam Agniveer Vayu Group X & XY Mock Test 01/2026 Mathematics Integral Calculus Properties of Definite Integrals
The functional I(y(x)) = \(\rm\displaystyle\int_a^b\)(y2 + \(\rm y^{\prime^2}\) + 2y sin x)dx has which of the following extremal with C1 and C2 as arbitrary constants?
1
y = C1e−x + C2ex − \(\frac{1}{2}\) sin x
2
y = C1ex + C2e−x + \(\frac{1}{2}\) sin x
3
y = C1e2x + C2e−2x − \(\frac{1}{2}\) sin x
4
y = C1e2x + C2e−2x + \(\frac{1}{2}\) sin x