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

Q: Use the table of integrals at the back of the text to evaluate the integrals ∫sin t/3 sin t/6 dt

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Q: Evaluate the integral. 7 sin?(t) cos“(t) dt

A:

Q: Given Tex+4 dx. Using a suitable trigonometric substitution, the resulting integral in terms of 0 is…

A: Given ∫19x2+4dx Let substitute x=23tanθ. dxdθ=23sec2θdx=23sec2θ Substituting the value, we get…

Q: Evaluate the integral. |sin° (x)cos“ (x)dx

A: In this question, the exponent of cos(x) is even i.e. 4, and the exponent of sin(x) is odd i.e 5,…

Q: Evaluate the integral. 4 dx +C (1 – x2)ž NOTE: Enter the exact answer, without any trigonometric…

A: This question can be solved by the concept of integration by substitution(without any trigonometric…

Q: use the indicated substitution to evaluate the integral.

A:

Q: Simplify the integral 1 dx using an appropriate trigonometric substitution. Va2 +4 Cos e do de sec 0…

A: Hence option (e) is correct.

Q: dx x Vx² +3 2

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Q: Supply the missing integrand and the limits of integration - 2sin 0 r cos?0 dr d0 = _d®

A:

Q: sin(6x) Vi? +4 dt 7

A:

Q: Evaluate the integral given. sec(2a)tan(2a)dx +C %3D

A: ∫ sec(x)tan(x) dx =sec(x)+C

Q: Can you help with this problem step by step?

A: Take out the 9 , because it is constant. Integration of sec^2 x is tanx

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: Complete the integration: sin3(2x) + C ? sin (2x) Ssin"(wcos (x)dx 16 32 Determine the value of "?".

A:

Q: Evaluate the integral. sinh? (x) cosh(x) dæ =

A: solve the integral

Q: find formulas for the functions represented by the integrals.

A:

Q: 10 Sin h (Ux)

A: we have to find integration

Q: What is the integral of sin? r cos x dx?

A: Given,           ∫sin2xcos2xdx

Q: 1 dx becomes: Using a trigonometric substitution, the integral x* V1-x? Select one: Jcsc* e de Sante…

A:

Q: Find the value of following the integral: ☎ COS²T -π1+a* S². dx,a>0

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Q: 1. a° cos(2)da = %3D

A:

Q: 2 sin? t sec“ t dt

A: To determine:

Q: The definite integral /. '(tan2(x) + sec2(x) ]dx when evaluated is equal to AV3 + Br, where A and B…

A:

Q: sin2(0) cos(0) d0, sin(0)

A:

Q: The value of the integral sin() dy dz is

A:

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

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Q: b) sec* 0 d0 Give the exact answer.

A: The given integral is ∫π4π3sec4θ dθ

Q: Find the value of the integral ∫∫R  and cos(x) cos(y) dA, where R=

A: We need to evaluate  ∫∫cos(x)cos(y)dA over region R=(x,y)| 0≤x≤π2,  0≤x≤π2

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

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

Q: Use the indicated substitution to evaluate the integral. 1 dx, x = 15 sec(0) xVx² – 225

A:

Q: 0. sin? x cos? x dx

A:

Q: valuate the integral. 10 sin?(x) cos3(x) dx CoS

A: Perform integration

Q: Evaluate the integral: 2 x2 ) dx (23+1)? Input answer as decimal. Round off to 2 decimal places.

A:

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: The definite integral | '[tan2(x) + sec2(x)]dx when evaluated is equal to A/3 +Br, where A, B are…

A:

Q: By using a trigonometric substitution x = 3sece ,where 0 s0 < 27 "he integral 3 Vx² - 9 dx can be…

A: We have to choose the correct answer from the given option according to the given condition

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

A: Given integral, ∫5816tan2x-16sec2xdx

Q: Given dx. Using a suitable trigonometric substitution, the resulting integral in terms of 0 is…

A: Given: ∫19x2+4dx Let I= ∫19x2+4dx To solve this we need to the trigonometric substitution

Q: x2 – 15 dx 23

A: Please rate

Q: dx 4ах

A:

Q: For an integral of the form f sin™(x)cos"(x)dx, saving one sine factor and converting the rest to…

A: Given data÷

Q: luate the integral. (Use C for the constant of integration sin(2x) xp 21 + cos?(x)

A: The integration of  sin(2x) / (21 + cos2(x)).

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

A: Use integration by parts

Q: Evaluate 4.x sin(y?) y3 dydx. Hint: reverse the order of integration

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Q: 03 cos(02) dO /2

A:

Q: d) S cos³x sin*x dx

A:

Q: Va dx (1+x)? 2

A:

Q: Which expression represents the midpoint approximation M3 to the integral r12 sin (/æ) dx?

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: Evaluate the integrals

A: We have to evaluate the definite integral: ∫-ππ1-cos2 t32dt We know the trigonometric identity, cos2…