# Fragen zur Integration und Vektoralgebra

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

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

dy/dx = x2 – 4x + 3

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

1. 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.
1. If the marginal cost of producing a product in a firm is:
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MC = 5q2 – 7q + 20,

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

1. Determine the customer’s surplus of a commodity at a price of N15 given that the demand function is p = 24 – q2.
1. 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

1. 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.
1. 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.
1. If A = 3i – 2J + k and  B = 2i + 3J – 4k
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Find:

• A . B and angle between the vectors A and B
• A x B
• |A| and |B|
• Hence find the angle between the vectors.
1. Find the vector product of the following:
• A = 2i + J and       b = I -3J + K
• (8,4,2) and       (6,4,-3)
1. If r = 3i – 2J + k
• Find the magnitude r
• Find the unit vector in the direction of r
• Calculate the direction cosine of r.
1. Show that p and q are perpendiculars where:

P = 3i – 4 J + 5k     and

q = 2i + J + 2k