1. Calculate the definite integral 1 (229-33 +5) de (a) Find an antiderivative F(x)= (b) Evaluate...
Name(PRINT): MAC 2233 Worksheet 10 1. Calculate the definite integral. % (223 -3. + 5) dx (a) Find an antiderivative F() (b) Evaluate F(2) F(2) (c) Evaluate F(1) F(1) = (d) Calculate the definite integral. (23- - 3.r+5) da 2. Calculate the definito integral. Give exact answers. 3e="é do (a) Find an antiderivative F() (b) Evaluate F(0) F(0) (c) Evaluate F(-1) F(-1) = (a) Calculate the definite integral. 3e
Use substitution to evaluate the definite integral given below. -- tan* (3*) sec* (33°) de (Enter an exact answer.) Provide your answer below: S. - x tan* (3x)secº ( 3x?) ck=
if x < 1 f(x) = { * if x > 1 Evaluate the definite integral. [ºs(x)dx f(x) dx Evaluate the integral –9|x? – 4x|dx Evaluate the integral $." (048 + x) as Integral =
Objective The usual procedure for evaluating a definite integral is to find the antiderivative of the integrand and apply the Fundamental Theorem of Calculus. However, if an antiderivative of the integrand cannot be found, then we must settle for a numerical approximation of the integral. The objective of this project is to illustrate the Trapezoidal Rule and Simpson's Rule. Description To get started, read the section 8.6 in the text. In this project we will illustrate and compare Riemann sum,...
Find f(x) if f'(x) = 177 and f(1) = 1 Evaluate the definite integral -, xe** dx
(a) The derivative of a function (b) The definite integral 3. Find the antiderivative: 1 x sin xdx 4. State the fundamental theorem of calcul 5. The position of an object moving on a
Use a change of variables to evaluate the following definite integral. 0 S xV81-x* dx -3 Determine a change of variables from x to u. Choose the correct answer below. O A. u=x4 O B. u = 81- x4 O C. u = 4x3 OD. u= 181 - x4 Write the integral in terms of u. S xV81-x* dx= du -3 Evaluate the integral. 0 5 x 181-x* dx= { -3 (Type an exact answer.)
x-5 dx. ) Evaluate the definite integral S 22-3x+2 Determine whether the improper integral S, dx converges. If convergent, find its value.
help please Evaluate the definite integral using the Fundamental Theorem of Calculus. (1+ (1 + 14х5) dx Use The Fundamental Theorem of Calculus and the antiderivative found in Step 2 to evaluate the definite integral. fo* (2 + 14x5) dx = = (x+3x0916 (1+](O* )-( O*+O) “) 10 3
Find the indicated integral. Check your answers by differentiation. 1) du The slope f '(x) at each point (x, y) on a curve y = f(x) is given along with a particular point (a, b) on the curve. Use this information to find S (x). 2) f'(x) = 9x2 - 8x + 2; (0,7) 2) A) f(x) - 3x3 - 4x2 + 2x - 7 B) Ax) = 3x - 8 C)/(x) - 9x3 - 8x2 + 2x + 7...