2020年12月21日 · In exercises 1 - 20, find the antiderivative \(F(x)\) of each function \(f(x).\) 1) \(f(x)=\dfrac{1}{x^2}+x\) 2) \(f(x)=e^x−3x^2+\sin x\) Answer \(F(x)=e^x−x^3−\cos x+C\) 3) \(f(x)=e^x+3x−x^2\) 4) \(f(x)=x−1+4\sin(2x)\) Answer \(F(x)=\dfrac{x^2}{2}−x−2\cos(2x)+C\) 5) \(f(x)=5x^4+4x^5\) 6) \(f(x)=x+12x^2\) Answer \(F(x)=\frac{1}{2 ...

Find the most general antiderivative for each of the following functions. 2. Find the values of the parameter A and B so that. (a) F(x) = (Ax + B)ex is an antiderivative of f(x) = xex. (b) H(x) = e2x(A cos x + B sin x) is an antiderivative of h(x) = e2x sin x. 3. A particle moves along a straight line so that its velocity is given by v(t) = t2.

Worksheet # 23: Antiderivatives 1. Find the most general antiderivative for each of the following functions. (a) x - 3 . 1 . 6 3 (b) 4x 5x + 9x (c) (x + 1)(9x - 8) (d).jX- 2 (e) x (f) # - 40 . x. 3 . 8x. 2 +5 (g) 5 (h) x. 6 (.).jX 3 . 3 . 1 -+-x . x. 2 . 4 (~) 2 5x. e. W (k) 1 x 3 (I) sin(fJ) - sec. 2 (fJ) 2. Find the values of the parameter A ...

2024年4月4日 · Solution. First, we find the general form ofy(x) by integrating y′(x). y(x) = Z 1 √ 64 −x2 dx= sin−1 x 8 + C. Next, we find the value of the constantCby using the initial condition y(−4) = 0. This gives sin−1 − 1 2 + C= 0 ⇒− π 6 + C= 0 ⇒C= π 6. Therefore, the solution of the initial value problem is y(x) = sin−1 x 8 + π ...

4.9 Antiderivatives Problem 1 Find the most general antiderivative of the function g(t)=e2t 5+6 p t 7 t + 5 11+t2 Problem 2 Assume that f0(t)=4t3 +2t and f(3) = 5.Findf(t). Problem 3 Given the graph of a function: (a) Sketch four anti-derivatives of the given function. (b) What is algebraic representation for the graph of given function f?

AP Calculus AB – Worksheet 46 Integration of Inverse Trigonometric Functions Evaluate each integral. 1. dx ³ x2 9 2. 9r2 1 r3 ³ dr 3. ³cos 3 4z dz 4. dx ³ sin2 3x 5. 2 x 6cos 2 sin t dt t ³ 7. 6. x 2 1 ³ dx 40 ³ x 25 8. dx 1 4x2 ³ 9. 2 2 41 y dy ³ y 10. dx 9 x2 ³ Answers: 1. 1 3 § ©¨ · ¹¸ tan 1 x ©¨ 3 · ¹¸ C 2. 6 1 r3 C 3 ...

MATH 122 Antiderivatives and the Indefinite Integral Use the rules for integrating polynomials, exponentials and logarithms to nd an antiderivative and then the inde nite integral of each of the following functions. Remember your exponent and logarithmic laws, these will help you. For any n 6= 1, Constant Rule R 0dx = C Power Rule R xn dx = 1 ...

Antiderivatives MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the most general antiderivative. 1) ∫ (6x3 + 9x + 2) dx A) 18x4 + 18x2 + 2x + C B) 18x2 + 9 + C C) 3 2 x4 + 9 2 x2+ 2x + C D) 6x4 + 9x2 + 2x + C 1) 2) ∫ (2x3 + 6x + 8) dx A) 6x4 + 12x2 + 8x + C B) 2x4 + 6x2 + 8x + C C) 1 2

Find the anti-derivative: 3. (a) Estimate the area under the graph of f(x) = x from x = 0 to x = 4 using four approximating rectangles and right endpoints. Sketch the graph and rectangles. Is your estimate an under or overestimate?

2024年4月4日 · Section 4.8: Antiderivatives - Worksheet 1.Evaluate the following antiderivatives. (a) Z 7 1+x2 dx (b) Z 3