The values of the following integrals are known and can be found in integral tables or by computer. Your goal in evaluating them is to learn about contour
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- By expanding (xh)2+(yk)2=r2, we obtain x22hx+h22ky+k2r2=0. When we compare this result to the form x2+y2+Dx+Ey+F=0, we see that D=2h,E=2k, and F=h2+k2r2. Therefore, the center and the length of a radius of a circle can be found by using h=D2,k=E2 and r=h2+k2F. Use these relationship to find the center and the length of the radius of each of the following circles. x2+y2+4x14y+49=0arrow_forwardFind the unknown value. 27. y varies jointly with x and the cube root of 2. If when x=2 and z=27,y=12, find y if x=5 and z=8.arrow_forward4. Evaluate the integral below by following a series of steps: 2x +3 J 4x² + 5x + 6 (a) Evaluate f dx by using trigonometric substitution. 4x2+5x+6 Hint: Pull a 4 out of the integral, then use "completing the square" in order to write the denominator as (x + A)2 - B 2. Then use a trigonometric substitution. 8x+5 (b) Evaluate f dx (Don't think too hard! The answer is easy!) 4x2+5x+6 (c) Find constants C and D which allow you to write the original in the following way: 8x +5 dx + D| 2x + 3 dx 4x2 + 5x + 6 dx = C J 4x2 +5x + 6 4x2 + 5x + 6 (d) Use parts (a), (b), and (c) to evaluate the integral!arrow_forward
- dx x² +9 2. Use an appropriate trigonometric substitution to rewrite J as J(a simplified trig function of 0) d0. Carefully show your work with differentials and use of trig identities to help simplify. Then find the integral. Show any use of substitutions and reasoning with right triangles.arrow_forwardPlease circle the answer and specify the answer so that I can understand. I sent this question before and it was answered incorrectly. Please write clearly so that I can read if you write by hand. I appreciate your understanding.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageIntermediate AlgebraAlgebraISBN:9781285195728Author:Jerome E. Kaufmann, Karen L. SchwittersPublisher:Cengage Learning