Set, Relation and FunctionHard

Question

Let f(x) be a function satisfying f′(x) = f(x) with f(0) = 1 and g(x) be a function that satisfies f(x) + g(x) = x2. Then the value of the integral f(x) g(x) dx, is

Options

A.
B.
C.
D.

Solution

f(x) [x2 - f(x)] dx
solving this by putting f′(x) = f(x).
Hence, (B) is the correct answer.

Create a free account to view solution

View Solution Free
Topic: Set, Relation and Function·Practice all Set, Relation and Function questions

More Set, Relation and Function Questions

f(x) and g(x) are two differentiable functions on [0, 2] such that f″(x) - g″(x) = 0 f′(1) = 2g′...In a class of 100 students, 55 students have passed in Mathematics and 67 students have passed in physics, no student fa...For every integer n, let an and bn be real numbers. Let function f : IR → IR be given by f(x) = , for all integers...Let R {(3, 3), (6, 6), (9, 9), (12, 12) (6, 12) (3, 9) (3, 12), (3, 6)} be a relation on the set A = {3, 6, 9, 12}. The ...Sets A and B have 3 and 6 elements respectively. What can be the minimum number of elements in A∪ B ?...