# Questions on Integration and Vector Algebra

**Integration** is another aspect of calculus. It is sometimes called anti-differentiation because it is the reverse of differentiation. You can attempt up to 22 questions on differentiation by clicking on this link.

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**What is Vector Algebra?**

A Vector is a quantity having both magnitude and direction. And since you can’t talk about Vector without mentioning Scalar, it would be good to note that Scalar is a quantity that has magnitude but one direction. **( kindly use the comment box below to ask a question).**

### Questions on Integration

- The gradient of a curve passing through the point (3,1) is given by:

dy/dx = x^{2 }– 4x + 3

Find the equation of the curve and the area enclosed by the curve, the maximum and minimum ordinates and the x-axis.

- The marginal revenue of a firm is found to be 15 – 4q. Determine the revenue function if from past sales the revenue was N1,250 when 28 units of the product were sold.

- If the marginal cost of producing a product in a firm is:

MC = 5q^{2 }– 7q + 20,

Find the total variable cost of producing the first 100 units of the product in the firm.

- Determine the customer’s surplus of a commodity at a price of N15 given that the demand function is p = 24 – q
^{2}.

- If the demand function for a product is p = 155 – 3q and the supply function is p = 7q – 20

Find:

- The equilibrium price and quantity.
- The consumer’s surplus.
- The producer’s surplus.

### Questions on Vector Algebra

- A security firm decides to sell four of its stocks. If the shares are 200, 150, 300 and 250 for stocks A, B, C, and D respectively and the selling price per share N200 for A, N100 for B, N300 for C and N250 for stock D. Calculate the total receipts from the stocks.

- Raphael Investment Limited decides to sell three of its stock. 300 shares of stock P, 400 shares of stock Q and 200 shares of stock R were sold. The selling price per share was N10, N8, and N5 respectively. Determine the total amount received from the sales of the stock.

- If
__A__= 3__i__– 2__J__+__k__and__B__= 2__i__+ 3__J__– 4__k__

Find:

__A__.__B__and angle between the vectors__A__and__B____A__x__B__- |
__A__| and |__B__| - Hence find the angle between the vectors.

- Find the vector product of the following:

__A__= 2__i__+__J__and__b__=__I__-3__J__+__K__- (8,4,2) and (6,4,-3)

- If
__r__= 3__i__– 2__J__+__k__

- Find the magnitude
__r__ - Find the unit vector in the direction of
__r__ - Calculate the direction cosine of
__r__.

- Show that p and q are perpendiculars where:

__P__ = 3__i__ – 4 __J__ + 5__k__ and

__q__ = 2__i__ + __J__ + 2__k__

## Other Mathematics Questions

- Co-ordinate Geometry
- Permutation and Combination
- Set Theory
- Empirical Probability
- Integration & Vector Algebra
- Differentiation

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