Directions: evaluate the following integrals sinx 4. S –- dx cosx./cos?x-25 3 5. S. dx secx -

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 (sin z + cos x) da using by term by term integration 0. Answer:

A:

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

A: Assume denominator to be something and then do the integration by parts to solve the question.

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

A:

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

A:

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

A: We know that, sec2x=1+tan2x∫secxdx=ln|secx+tanx|+c. We evaluate the given integral using the above…

Q: Q4 Find the integrals of the functions. (Answer Five only ) 3- )tan t sec?t dt dx 4- S: xV5x2-4

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: Evaluate the integral. 1/4 | 4 secx dx 1/4 I sec²x dx = [ O 4 sec x dx = (Type an exact answer.)

A:

Q: The integral S³ S S Sse x dx x²+√√x²-1-1 sece tane de sece - 1 cose d 1 - sino sine de 1 + cose…

A:

Q: x*dx Using trigonometric substitution technique, | the simplified integral after substitution is: x²…

A:

Q: Which integral represents the length of the curve y = cos x be- tween 0 and ? I V1 + cos? x dx, I…

A: the given equation of the curve is: y=cosx we have to determine which integral represents the length…

Q: 2. Evaluate the Trigonometric integral. C (a). S sin(2x) cosxdx. rT/2 (b). S cot?xcsc*xdx. T/4

A:

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

A: Given- ∫dx25x2+2 To Find- The va;lue of above integral using trigonometric substitution.

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

A:

Q: Which integral represents the length of the curve y = cos x between 0 and 7? V1+ cos? x dx, TV1+…

A:

Q: Evaluate the integral. S (sec r- sin r) dx

A: Please go through the attached solution. I hope that this solution will help you. Thankyou . Best…

Q: Q1/: Evaluate the Trigonometric integral m/4 V(1+ tan?x)3 dx -a/4

A:

Q: c) Seax.Sinbx. dx =? Calculate the integral

A:

Q: dx 4. Evaluate the integral by trigonometric substitution: , Væ²-9

A: We can find the integral using trigonometric substitution as below

Q: Evaluate the integral. (Use C for the constant of integration.) 9 cos?x sin 2x dx

A: This question is based on Indefinite Integral.

Q: 1. a° cos(2)da = %3D

A:

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

A:

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: sinxdx if Which of the following integrals is obtained? X = Jó 1+cosx こ ド」N

A:

Q: dx/(cos(x)-1) what is the answer to this integral? Use C for constant.

A: Use simple integration formula.

Q: evaluate the iterated integral

A:

Q: S sin y cos('/2) dy

A: ∫sinycosy2dy

Q: . Find the exact value of each definite integral. Do not use decimal approximation. dx V1-x² а. 3 b.…

A:

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

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

Q: Calculate the indefinte integral and explain what it is geometrically: ∫ cos(π/x)/x2 dx  ∫0π/2…

A: Since you have submitted two questions, we'll answer the first question. For the second question…

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

A:

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: valuate the integral using the Trigonometric Substitution metho x² (81-x²)3/²2 dx

A: Topic:- application of integration

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

A: Given integral, ∫5816tan2x-16sec2xdx

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

A:

Q: Find the following integrals: sin x (i) [sin' x cos? x dx dx sin (x+ a) (ii)

A: In this question, we need to find the following integrals.

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

A:

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

A: Use integration by parts

Q: Use integration by parts to find the integrals shares e) f sin? @ de f) esint sin2t dt 8) x²e-* dx…

A: Evaluation of the Integrals

Q: sec x+ cos x COS.X dx 2 cosx

A: Given query is to evaluate the integral.

Q: Evaluate 3. 12 tanx dx. S12tan'x 12 tan x dx =

A:

Q: Use integration by parts to evaluate the following integrals. Show how you get your answers. (а) /а?…

A:

Q: Sin 2 x cos xdX =? Xdx =? %3D X COS KINC

A:

Q: Evaluate the integral. NOTE: Enter the exact answer. cos (2.r) dx = + C

A: To evaluate :  given integral that is ∫ e3x cos2x dx

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

A: Given Data The integral is ꭍx²dx/(1- x²)3/2.   Let,

Q: I. Perform the following integration. 1. (sinh r) (coth²r + csch³ 2) dr sec³r tan r 2. dx √2+ secr…

A:

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

A: