Consider the
(a) Evaluate the integral using the substitution
(b) Evaluate the integral using the substitution
(c) Evaluate the integral using the method of partial fractions. For what values of
Want to see the full answer?
Check out a sample textbook solutionChapter 7 Solutions
Calculus: Early Transcendentals, Enhanced Etext
Additional Math Textbook Solutions
Precalculus
Thomas' Calculus: Early Transcendentals (14th Edition)
Calculus: Early Transcendentals (2nd Edition)
University Calculus: Early Transcendentals (4th Edition)
- Decide whether you can find each integral using the formulas and techniques you have studied so far. Explain. (a) ∫2dx / √(x2 + 4) (b) ∫dx/x√(x2 − 9)arrow_forwardEvaluate the definite integrals using properties of the definite integral and the fact that -6. f (x) dæ = 11, and g(z) dr = 2. (a) (b) (s(2) – 9 (2)) da = (c) (d) (5ƒ (x)+ 6g (x)) da =arrow_forwardEvaluate the definite integral two ways: first by a u-substitution in the definite integral and then by a u-substitution in the corresponding indefinite integral. (4 – 3x)°dx = iarrow_forward
- Evaluate the definite integrals using properties of the definite integral and the fact that 5 r5 f(x). da = -2, I f (2) dr = 9, and g(x) dz = 3. %3D 10f (2) dæ = Number -3 (a) Lf (x) dæ = Number -3 (b) 5 (c) 1. (f (2) – g (x)) d: Number 5 (d) 1. (3f (x) + 4g (xæ)) Numberarrow_forwardUse the Change of Variables Formula to evaluate the definite integral. (x + 1)(x² + 2x) dx (Use symbolic notation and fractions where needed.) (x + 1)(x² + 2x) dx =arrow_forwardBi Get the integral of the given function xp,arrow_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_forwardEvaluate the definite integrals using properties of the definite integral and the fact that 3 · [²³ƒ (2) a (a) (b) (c) (d) L2 3 1³ (2) f(x) dx = -5, |6f (2) dx = [Number 3 f(x) dx = [Number 3 [³ (ƒ (2) – 9 (x)) dx = [Number (2f (x) + 3g (x)) dx = Number 3 ³ [₁³9 (₂² f (x) dx = 9, and g(x) dx = 2.arrow_forwardSolve f(x)=g(x). What are the points of intersection of the graphs of the two functions? f(x)=x2−x+3; g(x)=2x2−5x−18 If f(x)=g(x), then x=negative 3 comma 7−3, 7. (Simplify your answer. Use a comma to separate answers as needed.) The point(s) of intesection of the two graphs is/are nothing. (Simplify your answer. Type an ordered pair. Use a comma to separate answers as needed.)arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage