**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 1:**

Solve the equation and find the solution xyp^{2} + (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 - c_{1} = 0.

Then take, yp + 1 = 0.

p = -1 / y

dy / dx = -1 / y

y dy = - dx

Integrating we get,

y^{2} / 2 - c_{2} = -x

y^{2} / 2 + x - c_{2} = 0

Final answer is (y + logx - c_{1}) (y^{2} / 2 + x - c_{2}) = 0.

**Answer:**

(y + logx - c_{1}) (y^{2} / 2 + x - c_{2}) = 0.

**Example 2:**

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

**Solution:**

Integrate with respect ot x, We get

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

= (2 + x)^{6} / 6 + c.

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

**Answer:**

∫ (2 + x)^{5}dx = (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.

Between, if you have problem on these topics Components of a Vector please browse expert math
related websites for more help on sample paper of class 8 cbse

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 (x^{2} + y^{2}) dy

**Answer: log (x ^{2} + y^{2}) = 2ay + c.**