Homework: a) Evaluate the following integrals 1) | xe3* dx x? sin x dx 3) x sin 2x dx

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: Use the indicated substitution to evaluate the integral.

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Q: Evaluate the integral (use the substitution) : cos x dp- 9 + sin? x a. 6lu mlp + sin' x| + C 1 b. 1…

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Q: Complete the table by identifying u and du for the integral. "(x) u = g(x) du = g'(x) dx | (tan(x))7…

A: ∫fgxg'xdx u=gx du=g'xdx ∫tanx7secx2dx u= du=

Q: Evaluate the integral: |x cosh x² dx sinh x +C 2 x sinh x? +C sinh x? +C x² sinh 2x +C

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Q: Suggest a trigonometric substitution for each integral, and then write the new integral that results…

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Q: Use the indicated substitution to evaluate the integral. -3 cos x sin (sin x) dx , u= sin x 3 sin…

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Q: Evaluate the integral. 9 dx V64 - Sx2 sin +C tan sin +C tan +C a eo

A: To evaluate the integral

Q: use a geometry formula to find the exact value of the definite integral  4x dx on the interval [0,b]

A: The given function is 4x with the interval [0,b].

Q: tan(x)dx, Ind: u = cos(z)

A: We have to calculate the given integral: ∫tan x dx We know the identity, tan x=sin xcos x Therefore,…

Q: Evaluate the integral. π/6 6 sec 2x dx T/6 | 6 sec?x dx = (Type an exact answer.)

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Q: Evaluate the integral. sech?x +C. 4 + tanh x

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Q: Using substitution with u= sin(2x), the definite integral | 4 sin³(2x)cos(2x)dx is equivalent to (A…

A: The given integral is ∫0π4sin32xcos2xdx.

Q: If the substitution in the integration by trigonometric substitution is z = 3 tan 0, what would be…

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Q: 2 sin? t sec“ t dt

A: To determine:

Q: dx When the integral ex4- e2x is evaluated by trigonometric substitution, the integrand is…

A: To simplify this integral, a substitution is taken. The first substitution taken is . This equation…

Q: Evaluate the indicated integrals if b is a positive real number constant. A. ftan () dx B. dx C.…

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Q: 5. Use trigonometric substitutions to evaluate the integral: I Væ(4 – #)dx.

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Q: Evaluate the integral si 3. sin° x adx. cos? 2

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Q: evaluate the iterated integral

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Q: Use the identity sin? x = 1– cos²x to write f sin?x cos?x dx a sum of two integrals and then…

A: To apply the reduction formula, substitute sin2x=1-cos2x, in the integral and simplify.…

Q: Example: Evaluate the following integrals. 1. / sin x cos" x dx 2. sin? x cos" x dx

A: To evaluate the following integral

Q: evaluate using Integration by Parts, substitution, or both if necessary.

A: Given integral is By using the following substitution, we get

Q: Evaluate the integral. x sec?(8x) da +C

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Q: 91. State whether the approximation MN or Ty is larger or smaller than the integral. (a) | sin x dx…

A: Since you have asked multiple questions, we can solve first question for you. If you want other…

Q: Evaluate the integral. 1/2 21 sin x dx

A: Integration is summation of discrete data. The integral is calculated for the functions to find…

Q: To evaluate the integral dx, we substitute x = 2 sec 0. VAx-4 Select one: a. True b. None of these…

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Q: Evaluate the integral J dx using trigonometric substitution. x²/16–a?

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Q: Evaluate the integral J x cot x² sin(in |sin x²l) d

A: To evaluate the integral: ∫xcotx2sin(ln|sinx2|)dx Solution: We know, ddx(f(g(x)))=f'(g(x)).g'(x)…

Q: The value of the integral (16 tan? x – 16 sec?x)dx %3D 5

A: Given integral, ∫5816tan2x-16sec2xdx

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: Evaluate the integral. 3 sin x dx +C |3D

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Q: Evaluate the integral J sin. sinh? (2x) cosh (2x) dx. sinf(2x) A +C 9. sinh(2x) +C B 8. costf(2x) +…

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Q: 3n/4 cot a In(sin r) dx

A: Use integration by parts

Q: Evaluate the integral sin3 x + cos? x + 1 dx sin? x (cos² x +1)

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Q: . Evaluate the integral Z (sin θ + cos θ) dθ.

A: Given that: ∫(sin θ + cos θ) dθ.

Q: Evaluate the integral. +C 17e" sin x dx || NOTE: Enter the exact answer.

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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))5…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 20 e dx x Inx

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Q: Evaluate the followaing integrals Li (1– 2sin?(x).sin(4x) dx) |

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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: (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 the following definite integral : , π/2 3 sinx cos x dx let u = 1 + 3 sin? x 1 + 3sin?,

A: Given,         ∫0π23sinxcosx1+3sin2xdx ;  Let u=1+3sin2x

Q: or the integral cosx sin'x dx ? Let u = There is more than one credit will be given.

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Q: To evaluate the integral 1 dx, we substitute (x2 + + 2x)3/2 x = sec 0- 1. Select one: a. False b.…

A: It is true.

Q: Is the integral formula correct? Sxsinx sin x dx = - xcos x+ sin x+C

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Q: use an appropriate substitution and then a trigonometric substitution to evaluate the integrals.

A: Given that, the integral  I = ∫x dx1+x4  Let t = x2  dt = 2x dx dt2 = x dx I = ∫x dx1+x4 I = ∫11+t 2…