11. Find the value of the integral dx. d) None of the above

Q: Use geometry and properties of integrals to evaluate the followingdefinite integrals.

A: Complete the square: (8x-x2) = -(x2-8x+16-16) => (8x-x2) = -(x-4)2 + 16 Substitute this in…

Q: J Sin (In 6) de

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Q: Evaluate the following integral. S cot 0 de

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Q: Consider S dx. Using trigonometric substitution, what is the integral fom in terms of 03

A: Given: ∫x2-9x3dx Using trigonometric substitution, we have to write the integral form in terms of θ.…

Q: Which of the following statements about integrals is true? sec(x) dx = tan(x) + C A tan(x) dx = In…

A: In this question, we need to find the correct statements.

Q: Which of the following integrals is equivalent to S 4 f tan? 0 sec OdO 2 f tan? 0 sec Odo 4 f sec? 0…

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Q: Given the following integral J csc2(8x) dx Use the integral table that was provided in class to find…

A: Given Data: Integrand: ∫csc28xdx The integral formula for cosecant function is, ∫csc2xdx=-cotx+C

Q: Evaluate the integral. 16 5x dx 0. O A. 480 O B. 320 O C. 40 640 OD. 3.

A: *to find:- integration. *formula:- int(x^{n}) = (x^{n+1})/(n+1)

Q: Use substitutions and the fact that a circle of radius r has an area πr^2 to evaluate the following…

A: ∫-π2π21-sin2x cosx dx Put, sinx=t⇒cosx=dtdx⇒cosx dx=dt When x=-π2, t=sin-π2=-1 When x=π2, t=sinπ2=1

Q: a) Evaluate the following integrals: eta TT/2 sin5e do tan 0 + tam30

A: ∫0π/2sin5θtanθ+tan3θdθ=substitute…

Q: In the integral, cos?tsin2tat , the correct u using general power formula is; A cost B sin(2t) ©…

A: Given integral is ∫cos2tsin2tdt =  ∫cos2t(2sintcost)dt = 2∫cos3tsintdt Now taking u = cost…

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

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Q: Evaluate the given indefinite integral. Indicate u, n, and du. [5an20 elan 20 sec? 2 Bdß

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Q: The approximation of the integral (x-4)ln (x+ 4)dx using two points Gaussian quadrature formula is:…

A: As per Bartleby's answering policy, we can answer only one question with a maximum of three…

Q: Find the integral of [(e exponE + 1].

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Q: For each integral shown below, determine the appropriate trigonometric substitution neces- sary to…

A: Convert the denominator of the given integral ∫x1-4x2dx in the form of a2-x2, and then use the…

Q: Using an appropriate substitution, the integral [x² x² csc²(x³) cot(x³) is equal to - dx - In…

A: Given ∫x2 csc2(x3)cot(x3)dx Formula: ddx(cot x)=-csc2xddx(xn)=nxn-1 Consider ∫x2 csc2(x3)cot(x3)dx…

Q: Which of the following integrals is equivalent to dy O none of these O 4f sec? 0 tan ed0 O 2 sec? 0…

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Q: Find or evaluate the integral

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Q: TU 5.fo cos³ 30 de

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Q: Which integral represents the length of the graph of y = In(x*) over the interval [1, e]: Select…

A: Given,  y = lnx2  We have to find the length of graph in the interval 1, e.

Q: Using trigonometric substitution, given (Vx+64 dx, the simplified form of the integral is: sec³ed®…

A: We have to check whether the given statement is true or false.

Q: x² +y? = 4, x² + y? = 9

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Q: Evaluate the following integral : S (sec X + cot X)² dx

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Q: The approximation of the integral (x - 5)'in(x + 5)dx using two points Gaussian quadrature formula…

A: We have to evaluate ∫-11x-52lnx+5dx using the two-point Gaussian quadrature formula. Now, the…

Q: The appropriate trigonometric substitution to evaluate the integral - z+3 dz is: Select one: O a.…

A:

Q: Using the Simpson's rule, the approximated value for the integral: f, dx, is equal to -3 O O O O O 0…

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Q: In the integral, Jcos²tsin2tat , the correct u using general power formula is; sin't sint None of…

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Q: In the given integral below, what is the values of u and a? ∫dx/√3-x^2 -2x u=x-1 and a=2 u=x-2 and…

A: the given integral is: ∫dx3-x2-2x we have to determine the value of u and a in the given integral.

Q: Sn/2 "/2 cot3 x dx

A: Given: ∫π4π2cot3xdx

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

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

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Q: (a) Estimate | V1- x² dx using the left end points of 4 equal intervals. (b) Knowing that the…

A: We have to find the approximation and value of integral.

Q: 14) Set the integral and find the area of one petal of r = cos 20 for - <o<.

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Q: The integral dx is Select one: O None. o o o

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Q: If the integral contains v(x^2 - a^2), the best trigonometric substitution to be used is A. let x =…

A: Solution is written in below steps.

Q: The integral of * x? dx is (x2+4)(x2+9) In(x? + 4) + In(x? + 9) + C Option 1 Option 2 -tan () + tan…

A: Given:     ∫x2dxx2+4x2+9 Perform partial fraction decomposition:     =∫95x2+9-45x2+4dx…

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

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Q: Evaluate the integral. *m/2 cos?(8) de

A: Let the given integral is, By using the constant-multiple rule By using the identity,

Q: Evaluate the integral. 13 dx 1 O A. 0 О В. - 13 13 Oc. -ze? O D. 13

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

A: We have to evaluate integral A = ∫π/43π/4cot2x +1 dx Using Fundamental theorem of Calculus,( F is…

Q: 55. Prove the formula SuT-zidx=;sin using geometry by interpreting the integral as the area of part…

A: We have given the integral;

Q: Find the integral. dx O A. 5x e* - In |x| +C O B. 5e* - In |x| + c 1 О с. 5ех. + C 2x? 2 O D. 5eX +C…

A: The solution is :

Q: Use the Substitution Formula, f(g(x)) • g'(x) dx = | f(u) du where g(x) = u, to evaluate the…

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Q: Complete the table by identifying u and du for the integral. u = g(x) du = g'(x) dx | (tan(x))?…

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Q: The integral o So e a dzdy is equal to 2a12, 2e a+4 2 a 4

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Q: In evaluating the inte gral, Substitution leads to a now integral S f(u) du xST+2x dx 1 Correct for…

A: Given∫012x21+2xdx

Q: Evaluate the given integral: cIn 3 e dx. 1+ezz

A: