Examples in Differential And Integral Calculus With Answers

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Examples in Differential And Integral Calculus With Answers
C S Charles Samuel Jackson
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Find for each of the curves given by the following equations, the area comprised between the curve, the axis Ox, and the ordinates X = \ and X = 10.
i» XL _ JL~r« _ 1 8. Find the area of the curve y^x = 4ta^2a - x) from a; = to X = 2a.
9. Draw the curves y = x and y = x\ Show in the case of either curve that the area bounded by the curve, the axes of x and y, and any ordinate, say a; = a, is finite, and calculate these areas for the two curves when the bounding ordinate is . T = 1.
10. Find the
... whole area of the curve ay + b^xf^ = a%^x^.
11. Let S be the slope of the chord of the curve y = a^ joining the points whose abscissae are x and x + h. Let A be the area of the graph of y = x^-'^ between the points whose abscissae are 1 and a. Find expressions for S and A, and verify that S = a'^ X A. What form does this result assume in the limiting case when h is infinitely small ? j Taking a = 2, obtain roughly the area of the graph of y ^ ~ X between x = I and a; = 2, by plotting the curve on squared paper and counting squares.


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