Concept explainers
Reduction formulas Use
45.
Want to see the full answer?
Check out a sample textbook solutionChapter 8 Solutions
EP CALCULUS:EARLY TRANS.-MYLABMATH 18 W
Additional Math Textbook Solutions
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
Calculus, Single Variable: Early Transcendentals (3rd Edition)
Thomas' Calculus: Early Transcendentals (14th Edition)
Calculus and Its Applications (11th Edition)
- 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 antiderivatives e* sinxdx A.je*(sinx – cosx) + c C. e*(sinx – cosx)+c Find the antiderivative A. ²/2 √x - √/12 + c B. e* (sinx + 2cosx) + c D. e*sinx + e cosx+c f(x - 1)√xdx 3 B. ²x² + ²x² + c c²x²-x+c 5 D. ²x²-3x² + carrow_forward3x2 dx . /1-x6 4. Evaluate 7x +C 3/1-x O cos (3x) + C O sin1(x³) + C O The antiderivative cannot be foundarrow_forward
- 4. 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_forwardWhat is the solution of the DE tan? x csc³ y dx = dy? cos³y A. tan x – x = cos y+ + c B. tan x = – cos y + cos³y + c cos3y + c C. x = - cos y + cos³y + c 3 D. tan x – x = - cos y + Answer: What is the order of y" + y" + y' + y = 0 A. Order 1 B. Order 2 C. Order 3 D. none Answer:arrow_forward• Evaluate the following integral: (use algebraic/trigonometric substitution) dx 1.f. (6-x²)z ·S= 2. 3. x² dx S 3 √x² + 16 dw w²√w²-4 4. 5. dx √ 2√x + √x 2x³ + 3x² 3 1²x³0 √1 + 2x³ SA) - dxarrow_forward
- dx 1. Maybe used: sin(x – y) = sin r cos y – cos r sin y J rVr² +x + 1 cosx 3. dr, Use z = tanr 3 cos r - 5 1 sec"-2 r tax+ п- 2 8. Derive the reduction formula / sec" r dr = sec"- dr. п — 1 -1arrow_forwardState the trigonometric substitution appropriate to finding an antiderivative for x2 (x2 +16)3/2. A. x= 64 tan 0 В. х%3D4 sес Ө С. х%3D 16 sec ® D. x = 4 tan earrow_forward(answer three only) Q4: Find the integration for the following functions: - sin(lnx) dx 2-5 3-S- In(x²+x)–Inx-e!nx dx -0 (1-сos2x) dx In(e(x+1)) 1- - 2 COsx 4- S csc²(cscx). dx sin?xarrow_forward
- Intermediate AlgebraAlgebraISBN:9781285195728Author:Jerome E. Kaufmann, Karen L. SchwittersPublisher:Cengage LearningCollege Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning