32. Sketch the negion whose area is given by the de finite integral ST-x* dx. Then use a geometric formala to evaluate the integral.

Q: а. Find the integral of e42 dz, where C is a circle z-2= 8 and x 1+ last digit of your ID.

A: In the given question we have to calculate the integral I=∮Ce4z(z-x)6dz where C is circle z-2=8 and…

Q: 4) Compute the integral where is the closed chrve SRe (z²)dz -2

A:

Q: 19) Use the trapezoidal lule and Simesons rule to apecox.mate the vale of the definite integral for…

A:

Q: 2. Use the form of the definition of the integral given in Theorem 4 (p. 380) to evaluate the…

A:

Q: Use the Residue to Evaluate the following Improper integral: dx x² + 2x + 2

A:

Q: Use the Residue to Evaluate the following Improper integral: dx x² – 2x + 2

A:

Q: Use the form of the definition of the integral given in the theorem to evaluate the integral. La (12…

A: According to the given information, it is required to evaluate the integral.

Q: Evaluate the integral.

A: Given: ∫e6dxxlnx. for finding this integral we use substitution method and  substitute lnx=t now we…

Q: B. Set up the integral for the area enclosed by y = 5x – x² and y = x from x =-2 to 6. Do not solve.

A:

Q: Use substitution to find the value of each indefinite integral. swers. x In et + 12 xp

A:

Q: 4) Show that the circumference of the unit circle is equal to 1 dx (an improper integral) 2 1 – x²…

A: We need to verify the circumference of circle.

Q: Evaluate the integral using Algebraic Sub. x + a dx 3x a |

A: Just I have used the substitution to make integral easy and then solved it. Final solution is in the…

Q: y5 dy; 4 + y*

A: The given integral is ∫y54+y4dy  ...... (1) Substitute u=y2 . This implies  y=u Differentiate u=y2…

Q: 3. Evaluate the integrals by interpreting them in terms of areas a) L(1+ v - ) 22 – x2 ) dx, b) 3

A:

Q: Use Simpson's rule to approximate the following integrals: (using n = 8 subintervals a. cos x³ dx

A: # as per the guidelines we are entitled to solve one question at a time, please resubmit the other…

Q: Evaluate the integral. |, arctan(1/x) dx (: -) * + In( *) 9. 2 O +In 2 4 (÷ - *) *+ In V3 8 n + 4 9.…

A:

Q: Evaluate the follocaing inde finite integrals using Substitution me thod . O Ssec (3x) tan (3x)dx

A: Explanation of the answer is as follows

Q: 8. Evaluate the integral x-1 dx by interpreting it as an area.

A: Area

Q: evaluate the integral using the methods covered in the text so far.

A:

Q: Estimate the following integral using the trapezoidal rule with n=10. 5² = 1+x² dx

A:

Q: u= 4-xneduce the ntegral to standand ferm Sonm dx 4-x)=

A: ∫x64-x72dx In this problem we need to reduce the given equation into standard form and solve the…

Q: Set up a definite integral, but do not evaluate, to find the area of the inner loop of the limaçon:…

A: The given curve is: rθ=2sinθ-1, θ∈[0,2π)

Q: Use this result to either evaluate the improper integral +oo 5xe dr or show that it diverges.

A:

Q: Get up the integrals equal to the area and the perimeter of the region S (ahaded in the figure…

A:

Q: Use the form of the definition of the integral given in the theorem to evaluate the integral. (18…

A: ∫3718-6xdx

Q: Show using residues that   the integral from 0 to infinity of dx/(1+x^6) equals (2pi)/3

A: We have to show that ∫0∞dx1+x6=2π3 by using residue theorem. Now, ∫Cdz1+z6=∫−RRdx1+x6+∫γdz1+z6 Now,…

Q: 4. Evaluate S,(x + 3)v4 – x² dx by writing it as a sum of two integrals and interpreting one of…

A: Given integral is ∫−22x+34−x2dx First , we will write the given integral into sum of the two…

Q: 1.5 x² In x dx

A:

Q: 14) ſe Vtanh® e" dy

A: Given that evaluate the integral

Q: Evaluate the following integrals using theFundamental Theorem of Calculus. Sketch the graph of the…

A: Fundamental Theorem of Calculus - If function f(x) is continuous over the interval a, b and F(x) is…

Q: Estimate the integral below by using Simpson's rule and Trapezoidal method with n=4, also find ET…

A:

Q: Evaluate the integral: S (in ce) dx = (8 ln(x))²dx 2 (x8) ( ×

A: Evaluate ∫lnx82dx=?

Q: Evaluate the integral by interpreting it in terms of areas. 2 + V 81 – x² ) dx 6-

A:

Q: Evaluate the following integrals using theFundamental Theorem of Calculus. Sketch the graph of the…

A: Given integral ∫1221-1x2dxwe have to evaluate the given integral using the fundamental therorem of…

Q: Jy cosy smy dy 3

A:

Q: By using u = In x, evaluate the integrals In x dx.

A: ∫x-1xlnx dx Now put, u=lnx⇒dudx=1x⇒du=1x dx

Q: 1. Evaluate (2 – x) dx by drawing a picture and interpreting the integral in terms of areas.

A:

Q: Evaluate the integral by interpreting it in terms of areas. V 25 - x2 ) dx

A: Given that, The integration is the following, I = ∫-50(4+25-x2)dx We have to find the value of this…

Q: 3) Use the definition of the integral to write n k п lim k k=1 n as an integral. Do not evaluate…

A:

Q: Which of the following integrals will represent the area outside r = 3, but inside r = 6 sin(0)?

A: area = 12∫ab[outer2 - inner2] dθ

Q: Evaluate the integral by interpreting it in terms of areas. *18 |x - 9| dx

A:

Q: What is the estimate of the integral using 4-segment Simpson's 1/3 Rule? 5+3x a. 0.14476 b. 0.10333…

A:

Q: z · 3°dz

A:

Q: (24 — бх) dx 14

A:

Q: Set up the integral to find the area inside r = 4 and outside r = 1.

A: Take a ring at a distance r = r  of width dr and find their area then integrate it over the given…

Q: Which of the following integrals represent the area enclosed by the smaller loop of r = 1 +2 sin 0?

A:

Q: Evaluate the integrals ∫2 cot πx dx

A:

Q: Compute the indicated integral by findng the area of the trapezoidal figure below. 110 4,0 F1 10 •5…

A: Given: A=∫35x+3dx

Q: Consider the integral 2x [2 dz. 4 Use the composite Simpson's rule with n=3 to approximate the…

A: