The Calculus

Ellery W Ellery Williams Davis

The book The Calculus was written by author Ellery W Ellery Williams Davis Here you can read free online of The Calculus book, rate and share your impressions in comments. If you don't know what to write, just answer the question: Why is The Calculus a good or bad book?

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-^o Vl - . 36 sin2 ^ > «^30o V5 - 2 sin2 a; Jo Vl^^ VT^^ 4. Show that n dx 1 p dx Jo 1 + 2 X cos <^ + x2 2 Jo 1 + 2 X COS (^ + x2 2 sin ' and explain what occurs when 0=0, and when ^ = ir/2. 5. Integrate the following general integrals; where /'(x) denotes the derivative of /(x). (a) j'/(x)/'(x)dx. Id) jr(2x)dx. (&) j"e*Ax)/'^x)dx. («) ij^^^' C ' ff\ ( f'{x)dx (c) J/'(cosx)sinxdx. U) J i + [/(x)]2* 6. "Verify the result of integrating sin^ x (?x by comijaring it with the integral of cos^ u du by means of the substitution u — 7r/2 — x. 7. Evaluate each of the following integrals : (a) I i &\n{u-\- v)dudv. (6) t I se'dtds. 8. Calculate the area ^, between the x-axis and the curve y = x^ — 9 x^ + 23 X — 15, from x = 1 to x = 3, by direct integration and also by Simp- son's Kule. Find the centroid (x, y) of the same area. VII, § 118] GENERAL EXERCISES 223 9. Proceed as in Ex. 8 for each of the following curves, between the limits stated below : (a) y = 1 + X — X- + x^ ; x = to a; = 2.

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