2) Use the properties of the definite integral to find the given integral, if possible, given that dx = 3, | f(x) dr = -1, and g(x) dr -5. | If(x) – 9(x)] dxr d) | f(r)g(x) dx | 7f(x) dr e) [f(x)+ 2g(x) – 2] d.æ c) / \f(2)° dr

Q: 10) Suppose that f is continuous and that f(z) dz = 0 and f(z) dz = 5. Find - 6f(x) dx . -3 -3 A) 30…

A: ∫-33f(z) dz = 0  ,    ∫-35 f(z) dz   = 5find -∫356f(x) dx∫abf(x) dx    = ∫acf(x) dx   +∫cb f(x)…

Q: dx 1 = S- g2+x2

A: Solve

Q: 4 Suppose | f(x)dx = 6, f(x)dx= 5, and g(x)dx = 8. Evaluate the following integrals. g(x)dx = 7…

A:

Q: 5 Find the following indefinite integrals. 10 a. f(x+2)' dx b. J d. [4 (3-&x) dx c. (3x-7) xp-

A: c)

Q: By the even extension method applied to the function f (x) = e¬16x, where x > 0, the value of the…

A: We have to solve given problem:

Q: Find the most general antiderivative of the function g(x) 3x2 -e + coS I | O 6x-ex-sin(x)+C O…

A: The given function,  g(x)=3x2-ex+cosx  .................................(1)

Q: 1. Find the definite integrals of the following functions : (a) L. 4.x dx (h) dx ex +1 -2 0. (b) /…

A: Since we only answer up to three sub parts. We’ll answer the first three. Please resubmit the…

Q: 15x²x³43x - 19 The integral (x + 1)²(x² - 6x +13) Ax + B What is the value of x²+bx+ca -dx? 3 A…

A: This is a problem related to integration. Based on the concept of partial fraction decomposition we…

Q: Evaluate the definite integral. ¤(x² + 7)°dx (b) / z x/1 – x²dx (a)

A:

Q: ₁√x³ √4-x² dx. if we let z = √√4-x², which of the following integrals is correct using rationalizing…

A: The given integral,        ∫x34-x2dx

Q: -1.30 Find the value of the integral 100 √x dx by using simpson method (n = 6)?

A:

Q: 1. If f(x) dx = 3, evaluate [[1 + 21(x)] dx using the properties of interga 2. If f(x) dx = -2 and…

A: As asked we can answer question no 1 and 4 as below.

Q: The integral 2a12 + 5x° is equal to -dx 3 x5 + x3 +1 (a) -25 + C (2) +2² + 1)* (b) z10 +C (1 + کے +…

A:

Q: * (Find the integral of e^2x c

A:

Q: 4. Find the exact values of each of the integrals below. f(x) (a) / f(æ) dæ (d) / F(2) dzæ 2 (b)…

A: We can see this function as f(x) = -x-5-4≤x≤-3-2-3≤x≤-22x+2-2≤x≤020≤x≤1x+11≤x≤2-3x+92≤x≤3-2x+63≤x≤4

Q: Evaluate the definite integral. 2 e 1/x* dx x

A:

Q: 4. If the integral value of | f (x)dx = 4 and | f(x)dx =-3 then the value of | f(x)dx is -1 -2 а. —3…

A: It is given that  ∫-14fxdx=4∫-24fxdx=-3

Q: A function is approximated by a cubic spline defined by: 25/12 30.0833 An approximation of ff(x)dx…

A: Sol:- Consider the function in the range of (0,1) ∫011+x+x2+x3dxApply the Sum Rule:…

Q: Given [ƒ(x) dx = -5, and g(x)= {x²-1,0≤x≤3 . Using the properties of (3x+2 ,3≤x≤5 integral. Find the…

A: Ans= -20  For detail...go through the solution...I have solved using given information in detail

Q: (a) Evaluate the integral 9x"e¬X dx for n = 0, 1, 2, and 3. n = 0 9. o((-") - (-1)) n = 1 е | n = 2…

A:

Q: Evaluate the definite integral (a) ľ² _l+ x +24 dx, (b) [¹² (x² + 3) (2x + 1)dx, (c) [¹ x²e²¹dx -1…

A: ∫-11 xdx1+x2+x4

Q: Evaluate the integral. J-Txe* dx -7(x +1)e -*+C a. O b. -7(x – 1)e*+C Oc. 7(x +1)e-*+C O d. 7xe-* +C…

A:

Q: x" e ax n-1 ax dx e ax dx Use one of the reduction formulas shown to the right (which are valid for…

A:

Q: How do I find K of the integral e^(x^2/2)dx on the bounds from 0-2 what is E_T? and what must n…

A: Given: The error in trapezoidal rule is given as:

Q: Demonstrate that for the function of the type va? + x2 you use the substitution X-atane and use it…

A:

Q: 9 Evaluate the integral f 2x (x² + 1)° dx using the substitution = x² + 1. и — с 2.x (x? + 1)° dx +C

A:

Q: The functions f and g are integrable and f(x)dx 2. f(x)dx 4, and g(x)dx= -3. Find the values of the…

A: Given, ∫24fx dx=−2,∫27fx dx=4 and ∫27gx dx=−3Concept used:1. ∫aafx dx=02.  ∫abfx dx=−∫bafx…

Q: To convert the integral dx into an integral of rational function of u is to use the substitution x =…

A:

Q: 15x²x³43x - 19 can be rewritten as (x + 1)²(x² - 6x +13) Ax + B C D Slax ² + + lax² + bx+c (mx + n)t…

A:

Q: (d) (x² + 1)² dx (e) L dx (x² + 1)² (f) eir dx

A: d. Given

Q: What must be the value of C (constant of x² - 4 -dx so that the x +2 integration) to the integral of…

A:

Q: The following integral is  The integral of g(x)dx from 7 to 2

A: The given integrals are,

Q: Sanna and Obadia argued about the definition of L e-x 1 dx - Sanna split the integral as -X e [54 dx…

A: We need to explain integral split.

Q: Given: ((x)dx Evaluate f(v2). There is a function f(x) such that when u = -x³, the resulting…

A:

Q: Given ~ √x³ √4-x² dx. Ⓒ-² (4-2²) dz Ⓒ√2 (4-2) 1/² d Ⓒ/(x++4+²) dz Ⓒ -√2² (4-2²) ³/2 dz dx. If we let…

A: topic- indefinite integral

Q: 1. Use properties of the definite integral to solve the following problem. f (x)dx = -3 and f(x)dx =…

A:

Q: 39.: * Compute the integral: x (Inx) dx. a. (5e –1) b. (3e -1) c. (e +2) d. (5e -e') (e* -e) 32 16…

A: Use by parts integration

Q: The value of the integral x'e*dx is e- 2e-1 а. - 2e- 3 e-2 b. 3 1- 2e с. 3 1- 2e d. 3 1+2e- е. 3.

A: Since you have asked multiple questions in single request so we  will be answering only first…

Q: Find the indefinite integral. a. -+c -7x + C e а. 1 b. -7x + C 7x 1 -7x - +C с. 7 d. -7e-1x + C e.…

A:

Q: Steb by step

A:

Q: find the following integral 2-3e^x / e^x dx;

A: We have to find the integral below:

Q: 1- The area under the curve y = sin?x over the interval [0 to 2n] is: A. В. п C. 2- The value of…

A: Explanation of the answer is as follows

Q: If g(1)=−5, g(5)=9, and ∫from 1 to 5 g(x)dx=−8, evaluate the integral ∫from 1 to 5 xg′(x)dx.

A:

Q: e 2x Evaluate the integral of e* +1 xp-

A:

Q: To evaluate the integral * dx we use the substitution e а. x2 1 O b. 1- x2 O d. x + 1 =t

A: Explanation of the solution is given below...

Q: The integral of the given function | 4sinxcos G) dx is equal –3 cos () – 6cos () А. + C 2 3 cos ()…

A:

Q: 3 Suppose that f(x) dx = 7, | f(x) dx = 5, and | f(x) dx = 10. %3D Evaluate the following definite…

A: (a) The given integral is: I=∫35f(x)dx As we know from the integral theorem,…

Q: 15x2-x3-43x - 19 dx Ax + B Jax? + bx + C D The integral can be rewritten as (x +1) (x² – 6x + 13)…

A: First we will find the values of A, B, a, b and c by the method of partial fraction.

Q: Evaluate the definite integral. (a) S, (x³ – 6x² + e-*)dx (b) S G+ 2)dx

A: a) ∫02x3-6x2+e-xdx=x44-6x33+e-x-102 Formula: ∫xndx=xn+1n+1 and ∫emxdx=emxm=x44-2x3-1ex02…

Q: = "+1 + C. 2. The power rule for integrals is x" dx a. Evaluate f da = fx2dx. n+1* 1 b. What goes…

A: