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

Q: 10. Prove by using integration by change in variable the ff. integral: dx :du 3D arcsecх+ С xVx2 – 1

A: We have given the integral ∫dxxx2-1 = I(say)     Put   x2-1 = t   ⇒x2= t2+1     Differentiate w.r.t…

Q: Use the Table of Integrals to evaluate the integral. (Use C for the constant of integration.) 5 sec2…

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Q: In ir le) secx dx to be integrable using the formula What should be the value of A for 2- sec x…

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Q: (3, 1) (у? + 2ху) dx + (- 1, 2) (x² 2ху) dy +

A: We have to show that the curvilinear integral is independent of path and we have to find its…

Q: by using the double integration, find the area that lies inside the curve r= (8cos e) and outside…

A: Given: The curves r=8cosθ    and r=4

Q: Evaluate the integral by making an appropriate change of variables. / 9 sin(49x2 + 64y2) dA, where R…

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Q: O Calculate He in tegual usng the Caucly Integral Theoren sin b (2) dz

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Q: a) By using integration by parts, find the integral Inx dx. b) Hence, find In Vx dx.

A: We have to apply the integration by parts.

Q: 1 -dx 2 xV 64 + 9x°

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Q: Use contour integration to compute the following integrals. (a) 1. 2π cos(20) dv 5+4 cos v

A: (a) Given integral ∫02πcos(2ϑ)dϑ5+4cosϑ. The objective is to compute the integral by using contour…

Q: S tan-3 (x) sec² x dx

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Q: Consider the integral sin(5z) d: Applying the integration by parts technique, let and du x dz Then…

A: The by parts formula of integration is ∫udv=uv-∫vdu.

Q: r430 sin x 160 cos2 x(16-sec² x)

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Q: Is the integral / A · dr path independent if A = (2x - у)i + (x + у)j? Evaluate A · dr around a unit…

A: The question has 3 subparts. 1st part requires the verification for path independence of a line…

Q: Using appropriate substitution, the integral *+imx) dx is equal to: an

A: From the given problem:   I=∫141+lnx3xdx...1   Substitute in equation (1).   1+lnx=u...Differentiate…

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: The area under the curve parametrized by x(t) = e", y(t) = 2et +1, where 0 St<1/3, is equal to.

A: As given, x(t) = e3t  y(t) = 2e3t + 1 where 0≤t≤13.

Q: Evaluate the integral and interpret it as the area of a region. я/2 |8 sin(x) – 8 cos(2x)| dx

A: Here this is a tricky question Find where the function is positive and where the function is…

Q: Using an appropriate substitution, the integral Jez-tan is equal to 2-tan sec²0 de O none of the…

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Q: Consider -(x Using a suitable trigonometric substitution, the resulting integral in terms of 0 is…

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Q: dx sin (7x)[7-cot2(7x)]

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Q: Evaluate the integral using Integration by Parts. | 2z? cos 5z dz

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Q: Use integration by parts to find the integrals.

A: To evaluate the integral by parts ∫x+2 sinx dx Integration by parts is done when there is a product…

Q: ® Evalnate Sin? (2x) Cos (om) da

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Q: 2. Consider the integral ² si sin redr which can be computed exactly. a) Apply Romberg integration…

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Q: m, nEN imperding cosM X sin x tor Integral obtain re duction formula. u sing this Calalate integrol.…

A: Topic : integration

Q: Evaluate the integral using integration by parts. Sox sec?2x dx Joxe 8x sec22x dx = (Type an exact…

A: Given:

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: If I, = Sx" cos x dr, by using integration by parts, prove that In = x" sin r + na"- cos r – n (n –…

A: We use integration by parts to show given condition.

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

A:

Q: 5. The volume of a sphere of radius 3 is 36x. What is the value of each of the following integrals?…

A: (a)∫0π∫0π∫03p2sinϕdpdϕdθ = ?We can write it as - ∫0π∫0π∫03p2sinϕdpdϕdθ =…

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

A: Given integral, ∫5816tan2x-16sec2xdx

Q: The suitable substitution to evaluate the integral (V cot (2x) dx is sin (2x) Ou3tan(2x) none Ou=…

A: To find The suitable substitution to evaluate the integral.

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

A:

Q: Evaluate the integral by making an appropriate change of variables. 2 sin(25x2 + 36y2) da, where R…

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Q: The suitable substitution to evaluate the integral cot (2x) dx is sin (2x) O u= tan(2x) O u= csc(2x)…

A: Integral is given

Q: Using a trigonometric substitution, the integral -dx becomes: R+25 Ss tan (@)de 5 tan?(@) de sec e S…

A: In the question we have to find value of integral after Trigonometric substitution.

Q: Use the trigonometric substitution r 2 sin 0 to compute the integral -2 VA – r² dx

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Q: Approximate the integral | dx using 4 trapezoids .2 1

A: Introduction: The formula for the trapezoidal rule is given by, ∫aby(x)dx=h2y0+yn+2(y1+y2+...+yn-1)

Q: Is the integral / A · dr path independent if A = (2x - y)i+ (x + y)j? of Evaluate A · dr around a…

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Q: Using integration by parts, the integral f In(16x*) dx is equal to:

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Q: Find the area under one arch of the trochoid x 70-1 sin(0), y = 7–1 cos(0).

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Q: sin't caso de V1 + sin A

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Q: Consider the integral sin-'(5x) dæ: Applying the integration by parts technique, let U = and dv dx…

A: Integration by parts is expressed as If I=∫f(x)⋅g(x)dxThen I=f(x)∫g(x)dx  - ∫ddxf(x)⋅∫g(x)dxdx Here,…

Q: Evaluate the triple iterated integral. ,3 xyz dx dy dz

A:

Q: Evaluate the given integral (2z+1) dz where the contour C is given in the figure,

A: In this question, we use the path for the integral  ∫C(2z+1)dz where C is the path given in the…

Q: Use the table of integrals to evaluate the integral. (Use C for the constant of integration.) 9 sec²…

A: This question can be solved using the concept of integration by substitution.