Jse the fundamental theorem of calculus part 2 to evaluate the integral: 3 S (8 sin x) dæ. Note: Round to the nearest thousandth.

Q: (b) Use the Fundamental Theorem of Calculus to evaluate the integral .8 So da dx x-6 x+8

A: Need to use the fundamental theorem of calculus to solve this integral.

Q: ot t/1 – sin² t dt, 0<t< w/2

A:

Q: Evaluate f dx letting u = x – 1. The given integral can be transformed to S h(u)du. What is the…

A: evaluate ∫xx-1dx letting u=x-1.The given integral can be transformed to ∫h(u) du what is the value…

Q: Evaluate the integral. NOTE: Enter the exact answer. 1 X for fo (ory + 173 dy d 1)² dy dx =

A:

Q: Evaluate the following integrals. 2 (a) S(csce)(1 + sin´e + sine cot + sin¯0 + sin0 cot¯0 ´e)de

A: Solution is given below:

Q: 36 - Evaluate the integral: dx (A) Which trig substitution is correct for this integral? Ox = 6…

A: Given that: ∫3x2-36x4dx

Q: dz "The integral S is a definite integral " 2-4

A: we have to subtitute x = 2 sec u  then find the integral using  ∫Secxdx=|nsecx+tanx

Q: If f(2)dx: f(x)dr, what are the bounds of integration for the first integral? a = and b = Question…

A:

Q: Evaluate the multiple definite integral J, J. zr²sinu du dr dz

A:

Q: N/= (2+V1-x²)dx= %3D Hint: interpret the definite integral as an area. 4+ TI+8 2+ I 4 O 4 2+ T

A:

Q: S)Use the Fundamental Theorem of Calculus to decide if the definite integral exists and either…

A:

Q: a) Evaluate the integrals using appropriate substitutions. dx Sino i)S i) f de Cos? 8+1 1+16x2

A: as per our guidelines I am solving only first question with both parts a(i) ∫dx1+16x2ii ∫sinθcos2θdθ

Q: Evaluate the integral. NOTE: Enter the exact answer. c10 1 xe"y dy dx

A:

Q: Evaluate the definite integral So [(sect tant) i + (tant) j + (2 sin t cost) k] dt

A:

Q: Use the Table of Integrals to evaluate the integral. (Use C for the constant of integration.) 5 sec?…

A:

Q: Evaluate the definite integral. rn / 2 csc(t) cot(t) dt T / 4

A: The integration of cosecant cotangent is of the form ∫csc(x)cot(x)dx=–csc(x)+c

Q: |a" cos(2°) da = +C. %3D Hint: First make a substitution and then use integration by parts to…

A: Consider the given integral ∫x11cosx6dx. Let u=x6. That implies, du=x6dxdu=6x5dxdx=du6x5 Then, the…

Q: et dx 9 + e" Evaluate the integral using the substitution u = 9+ e". et dx 9 + e* +C

A:

Q: Evaluate the integral. NOTE: Enter the exact answer. dy dx Jo (xy+ 1)²

A:

Q: Evaluate the integral: - S- de. 4- sin?e cose A None of the given choices ® sin-(ino) +c B Sin-1 ©…

A: The objective is to evaluate the integral.

Q: | (++3) et/4 dt

A: Here we will use integration by part formula

Q: Evaluate the definite integral?

A:

Q: e) Apply the Fundamental Theorem of Calculus in order to evaluate the definite integral: + 2)* dz =

A:

Q: 3. Use the Fundamental Theorem of Calculus Part 2 to evaluate the integral, or state why the…

A:

Q: Evaluate the integral. NOTE: Enter the exact answer. 1 xy* dy dx

A:

Q: dt J tan t/4 – sin? t

A:

Q: Evaluate the integral. NOTE: Enter the exact answer. xe* dy dr =

A: We have to evaluate the given integral- ∫08∫01xexydydx Here we will use the following formulas-…

Q: Transform the integral fo So? sin o sin 0 do do by the substitution r = sin o cos 0, y = sin o sin 0…

A: Given ∫0π2∫0π2sinϕsinθdϕdθand x=sinϕcosθ, y=sinϕsinθ

Q: A Click Submit to complete this assessment. Question 5 1-x²)dx= | Hint: interpret the definite…

A: We can use the method of substitution to solve given problem. Or  Solve it by using area.

Q: sec? e de. 1- tan e Evaluate the improper integral:

A:

Q: - sin(y) dy: cos(y) + 7 Consider the integral- This can be transformed into a basic integral by…

A:

Q: Set up - simplify a little bit, but do not evaluate y = sin x- I cos z for 0 < x <T/2. the integral…

A:

Q: nd the exact value of the integral using formulas from geometry. 2 2 dx 4-x dx = Type an exact…

A: Given query is to find the value of the integral using trigonometric substitution.

Q: V4 the integral | -dx, becomes O None cot2 (0)d0 tan? (0)de cos? (6)de 4 sin (0)de

A:

Q: Evaluate the integral. */6 6 sec?x dx R/6 S 6 sec?x dx =| (Type an exact answer.)

A:

Q: HW/calculate the integral the following -S e-st tan(t) dt

A: Given that, ∫0∞e-sttant dt From 0 to ∞, The e-sttant is increasing function.

Q: Evaluate the integral sec 0 tan e de. Answer:

A:

Q: To evaluate x?V1– x²dx using trigonometric substitution, what is the new integral in terms of .a? 1…

A: Simplify the integrand using the formulas below .   sin2θ=2sinθcosθsin2θ=1+cos2θ2sin2θ+cos2θ=1

Q: Which of the following statements about integrals is true? | csc(x) dx = cot(x)+C A cot(x) dx = ln…

A:

Q: Evaluate the integral from 0 to pi/2 6 sin5(t) cos(t) i + 3 sin(t) cos2(t) j + 8 sin(t) cos(t) k

A: Given:  ∫0π26sin5tcosti+3sintcos2tj+8sintcostkdt To determine: The value of given integral.

Q: (a) Consider the integral dx. Why can't this integral be computed using the Fundamental Theorem of…

A: Solution for a: Given integral is ∫-111x2dx We can write the above equation as…

Q: evaluate using trigonometric substitution. Refer to the table of trigonometric integrals as…

A:

Q: Find the integral. Check your answer by differentiation. | t cos(t?) dt

A:

Q: T/4 Evaluate 2 sec *0 d0.

A: Here we are using integration by substitution method after applying some basic trigonometric…

Q: r2 lex |e* – 1| + (e* + 1) dx J-1 ex

A:

Q: Jse the Fundamental Theorem of Calculus to evaluate (if it exists) f(z) dz, where S-5z 16 sin(z) if…

A:

Q: What is the value of the integral f sin(6z) arctan(sin 3r)dr? a) 3(7 – 2) b) c) d) 6(* - 2) e) - 3

A: Let  I=∫0π6sin(6x)·tan-1sin3x dx =∫0π6(2sin3x·cos3x)tan-1sin3x dx   ∵sin2x=2sinx cosx Assume,…

Q: Find the exact value of the integral using formulas from geometry. + 2x)dx 1 3 J(1+2x)dx =O…

A: Area of rectangle= length* breadth Area of triangle= 1/2 base * height

Q: b) Find the value of a such that the value of the integral /" ecos(?) sin(t) dt = 0 Answer: I =

A: