Evaluate the integral using the Fundamental Theorem of Calculus, Part I. | (10x° + 25x15) dx (Express numbers in exact form. Use symbolic notation and fractions where needed.)

Q: Write the integral in terms of u and du. Then evaluate. 18 sec? (x) tan (x) dx, u = tan (x) (Use…

A: Take substitution of u = tanx

Q: Evaluate the integral using an appropriate substituti NOTE: Enter the exact answer. x²e-&g³ dx = +C

A: Given that: ∫x2e-8x3dx

Q: 1 - √xdx

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Q: (b) Use the Fundamental Theorem of Calculus to evaluate the integral 8 x-6 So ²x+8 dx

A: Use fundamental theorem of calculus to evaluate the integral.

Q: (a) Evaluate the integral | 16х -dx by using substitution. 8x +2 (b) Evaluate the integral using by…

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Q: Evaluate the integrals using fundamental theorem. Write answer as exact value not approximation. a)…

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Q: Evaluate the following integral using the Fundamental Theorem of Calculus. 2s - 6 ds

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Q: 3) Evaluate- TC S 2co. CO

A: Given: ∫0π2cosx3-2sinx6dx

Q: Evaluate the integral using NOTE: Enter the exact answer. sec(7x) tan (7x) dx = appropriate…

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Q: Use the Fundamental Theorem of Calculus to evaluate the following definite integral:

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Q: Evaluate the integral using any appropriate algebraic method or trigonometric identity. Sce tan x)d…

A: To evaluate:∫cscx-tanx2dx

Q: Use the form of the definition of the integral given in the theorem to evaluate the integral. (x2…

A: Given:

Q: evaluate the integral by interpreting it in terms of area

A: Given,

Q: Evaluate the integral with the aid of an appropriate u-substitution. Simplify the answer, if…

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Q: Write the integral in terms of u and du. Then evaluate. | 12 sec (x) tan (x) dx, u = tan(x) (Use…

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Q: Evaluate the definite integral by expressing it in terms of u and evaluating the resulting integral…

A: Substitute u = 4x, Differentiate the above, du = 4dx dx=(du)/4

Q: tan r sec r

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Q: Evaluate the integral. .5 11) 6x5 dx -1 A) 624 B) 93,744 C) 15,624 D) -15,624 must show work…

A: Given ∫-156x5dx The Fundamental theorem of integral calculus  ∫abfxdx=Fb-Fa,  If F'x=fx

Q: (x² – 3x}dx 170.

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Q: Evaluate the integral using the Fundamental Theorem of Calculus, Part I. - 2611/3 dt 2814/3 8/27 t2…

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Q: Let the integral be 'solvable' using trigonometric substitution. What is the correct choice of u…

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Q: Evaluate the integral. A/2 sin!'(0) cos (0) de COS Jo

A: Given : ∫0π2sin11(θ)cos5(θ)dθ ∫0π2sin10(θ)sin(θ)cos5(θ)dθ∫0π2sin2(θ)5sin(θ)cos5(θ)dθwe know that…

Q: Using Wallis' Formula, find the value of the integral of cos8 3xdx using the limits 0 to π/6

A: We are given: cos8 (3x) and we have to integrate this using Walli's formula using limits o to π/6

Q: Evaluate the integral using the Fundamental Theorem of Calculus.

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: -In 3 x'e-*dx

A: ∫x2 e-x dx=x2·∫e-x dx-∫dx2dx·∫e-x dx dx=x2·e-x-1-∫2x·e-x-1 dx=-x2 e-x+2∫x e-x dx=-x2 e-x+2x·∫e-x…

Q: Evaluate the integral. tan -(7x) dx + C NOTE: Enter the exact answer in expanded form.

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Q: Evaluate the definite integrals exactly using the fundamental theorem of calculus. A) ſ, x+ vx dx =…

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Q: Evaluate integral 8 to 2 (4x + 3) dx in two ways:(a) Using area and geometry.(b) Using the…

A: Given:

Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. S sec² x 81 -…

A: The given integral is: I=∫sec2x81-tan2xdx    ...1   As we know the common integral.…

Q: Evaluate the integral using the Fundamental Theorem of Calculus. xp

A: Given that a finite integration and we find the value of this using fundamental theorem of calculas.…

Q: Evaluate the integral in terms of inverse hyperbolic function x2 dx Vx² + 1

A: for a part see 2nd,3rd and 4th step. for b part

Q: Evaluate the integral.

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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: Write the integral in terms of u and du. Then evaluate. 15 sec?(x) tan?(x) dx, u = tan(x) (Use…

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Q: Evaluate the integral. Hint: Use Trig Identities. ( 9 sec 0 tan 0 de

A: ∫9secθ tanθ dθ=9∫1cosθ·sinθcosθ dθ      ∵secx=1cosx  &  tanx=sinxcosx=9∫sinθcos2θ dθ Now put,…

Q: Use the form of the definition of the integral given in the theorem to evaluate the integral. 7 (x2…

A: Given,           ∫17x2−4x+7dx

Q: 7. 8 sin* x dx

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Q: Use the Fundamental Theorem to calculate the definite integrals. 2 1 dx x+2 -1

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Q: Evaluate the integral using Part 1 of the Fundamental Theorem of Calculus. 4 4x(1 – x)dx =

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Q: Evaluate the definite integral exactly, using the Fundamental Theorem. / (1² + 4x + 3)dx =

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Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. | cos (5t)…

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Q: Use the form of the definition of the integral given in this theorem to evaluate the integral. 1 | 3…

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Q: Use properties of the integral and the formulas in the summary to calculate the integrals.

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

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Q: Evaluate the integral by interpreting it in terms of areas. Draw a sketch. (geometrically) 5) Ix -…

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Q: Write the integral in terms of u and du. Then evaluate. 16 sec2 (x) tan (x) dx, u = tan(x) (Use…

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Q: Evaluate the integral using the indicated trigonometric substitution. (Use C for the constant of…

A: Given integral , ∫x3x2+36.dxLet us take indicated trigonometric substitutionx=6tanθdx=6 sec2θdθ

Q: Evaluate the integral using only methods taught in class, and simplify your answer. Do not ski…

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Q: Evaluate the integral using appropriate substitution. an NOTE: Enter the exact answer. dx +C…

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Q: Evaluate the integral using the indicated trigonometric substitution. (Use C for the constant of…

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