Test: Integrals- Assertion & Reason Type Questions - JEE MCQ

This is a standard integral and hence R is true.

Hence A is true and R is the correct explanation for A.

⇒ log y = x log x

Differentiating w.r.t. X

Hence R is true.

Since

Using the concept of anti-derivative, A is true.

R is the correct explanation for A.

Adding equations (i)+(ii),

∴ I = π/4

Hence R is true.

From (ii), A is also true.

R is the correct explanation for A.

This is a standard integral and hence true. So R is true.

Hence A is true and R is the correct explanation for A.

∫e^x [f(x) + f′(x)]dx = ∫e^xf(x)dx + ∫e^xf′(x)dx

= f(x)e^x - ∫f′(x)e^xdx + ∫f′(x)e^xdx

= e^x f(x) + c

Hence R is true.

∫e^x(sin x - cos x)dx = e^x (-cos) + c

= -e^x cos x + c

Hence A is false.

∴ A is true

which can not be integrated.

∴ R is false.

f(-x) = (-x)³ + 5

= -x³ + 5

f(x) is neither even nor odd. Hence R is false.

Hence A is true.

This is a property of the definite integrals and hence R is true.

Hence A is false.