Infinite Integral Exam

Indefinite integrals are general integration method. Indefinite integral is the inverse method of differentiation method. Indefinite integrals have the constant value in the resultant value. The constant value is denoted as C. Different values of C will give different integrals. Thus, the function is called as indefinite number of integrals. Because of this property, it is called indefinite integrals. Generally integration of a function r(x) is denoted as R(x) = ? r(x) dx.

Example problems on indefinite integrals exam

Exam problem 1:

Integrate the given equation ? 4vx dx.

Sol:

Given equation is ? 4vx dx.

Rearrange the given equation as, ? x(1/4) dx.

Integrate the given equation with respect to x, we get

? 4vx dx = ? x(1/4) dx.

= x (5 /4) / (5/4) + c

= (4 / 5) x (5 / 4) + c

Answer:

The final answer is  (4 / 5) x (5 / 4) + c.

Exam problem 2:

Integrate the given equation ? 7x dx

Solution:

Given equation is ? 7x dx

Integrate with respect to x, we get

? 7x dx = (7x / log 7) + c

Answer:

The final answer is (7x / log 7) + c

Exam problem 3:

Integrate the given equation ? (1 -2x) (3 + 4x) (5 - 3x) dx

Solution:

Given equation is ? (1 -2x) (3 + 4x) (5 - 3x) dx

First expand the given equation, we get

= ? (3 + 4x - 6x - 8x2) (5 - 3x) dx

= ? (3 - 2x - 8x2) (5 - 3x) dx

Integrate with respect to x, we get

= ? 15 dx - ? 19x dx - ? 34x2 dx + ? 24x3dx

= 15x - 19x2 / 2 - 34x3 / 3 + 24x4 / 4 + c

= 15x - (19 / 2)x2 - (34 / 3)x3 + 6x4 + c

Answer:

The final answer is 15x - (19 / 2)x2 - (34 / 3)x3 + 6x4 + c.

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Practice problems for indefinite integrals exam

Ex:1 Evaluate the exam problem ? sin-1 cosx dx

Ans: (3.14 / 2) x - (x2 / 2) + c

Ex:2 Evaluate the exam problem ? (3cotx - 2tanx)2 dx

Ans: 4tanx - 9cosx - 25x + c

Ex:3 Evaluate the exam problem ? (7x2 - 3x) dx

Ans: (7 / 3) x3 - (3 / 2) x2 + c