Introduction to learn for calculus exam questions:

Calculus exams are mostly consists of differentiation and integration questions. Calculus mainly used for differentiation and integration. The integral calculus is concerned with the inverse problem namely given the derivative of a function to find the function. Calculus is one of the best methods to find the area of the region and used to find the rate of change of the equations.

 

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Example problems for calculus exam questions

Example 1:

Solve the equation and find the solution xyp2 + (x + y)p + 1 = 0.

Solution:

Factorising the above equation we get,

(xp + 1)(yp + 1) = 0.

xp + 1 = 0 and yp + 1 = 0.

First take, xp + 1 = 0.

                      xp = -1

                        p = -1 / x

Here, p = dy / dx

                      dy / dx = -1 / x

                          dy = -dx / x

Integrating we get,

            y + logx - c1 = 0.

Then take, yp + 1 = 0.

                         p = -1 / y

                dy / dx = -1 / y

                    y dy = - dx

Integrating we get,

                    y2 / 2 - c2 = -x

                  y2 / 2 + x - c2 = 0

Final answer is (y + logx - c1) (y2 / 2 + x - c2) = 0.

Answer:

(y + logx - c1) (y2 / 2 + x - c2) = 0.

Example 2:

Integrate the given equation with respect to x. ∫ (2 + x)5dx

Solution:

Integrate with respect ot x, We get

∫ (2 + x)5dx = (2 + x)(5 + 1) / (5 + 1) + c.

                    = (2 + x)6 / 6 + c.

Final answer is (2 + x)6 / 6 + c.

Answer:

∫ (2 + x)5dx = (2 + x)6 / 6 + c.

Example 3:

Integrate the given equation with respect to x. ∫ (3 - x)2/3 dx

Solution:

Integrate with res pect to x, We get

∫ (3 - x)2/3 dx =  (3 - x)(2/3 +1) / (2/3 + 1) + c.

                       = (3 - x)(5/3) / (5/3) + c.

                       = 3/5 (3 - x)(5/3) + c.

Final answer is 3/5 (3 - x)(5/3) + c.

Answer:

∫ (3 - x)2/3 dx = 3/5 (3 - x)(5/3) + c.

 

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learn for calculus exam questions-Practice problems

1) Integrate ∫ sin 3x cos 2x dx

Answer: -1/10 (cos 5x + 5 cosx) + c.

2) Integrate ∫ sin3x dx

Answer: 1/4 (-3 cosx + (cos 3x/3)) + c.

3) Solve x dx + y dy = a (x2 + y2) dy

Answer: log (x2 + y2) = 2ay + c.