r² (x²– 1)(x² + 1) , What is the resulting value of the definite integral dx? х-1 O 33 1 + 4 15 O 31 1 14 1 +9 2 4 3 O 31 1 + +7 O 33 1 1 + 15 2 5 4 +

Q: * t/3 Evaluate the integral S'(y cos x – 3) dydx. S x -

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Q: c) 1/2 1 1-x² dx

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Q: Use Part 2 of the Fundamental Theorem of Calculus to evaluate the definite integral. a) S(1 + 3x –…

A: "Since you have asked multiple questions, we will solve the first two questions for you. If you want…

Q: 5. Use Green's theorem to evaluate where C is shown below (6y - 9x) dy — (xy - x³)dx (-1,4) (-1,-1)…

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Q: x-2 Evaluate the integral S (t³ In ti + 3t³ sin (t*) j+ k) dt. x(x+1)

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Q: Q3/ Evaluate the integral: TT ° cos(x²)dx dy

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: S(2- sec2x) elmale sec³x sec(3A – x) e ln (xle) What should be the value of A for dr to be…

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Q: 4 x Calculate the integral: dx 72 6, 2 x a) O 3 +C 18 arcsin b) O-2 aV9 – x² + 18 arcsin )+c 2 x c)…

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Q: Evaluate the indefinite integral. 2 (t) – 7e' + 8 + 1 + 12 2 sin(t) – 8 cos(t) + sec- dt = +C.

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Q: 4- 2x Evaluate the following integral : dx 2x +4,

A: The answer is π/3.

Q: dx integralini hesaplayınız. 1-x3

A: Evaluation of integral

Q: 1. Evaluate the following integral: (1-e-²x) dx (a) analytically;

A: Note:- For this problem all the sub-parts  are different as methods are different. So, we can solve…

Q: 1. Evaluate the given integral Q. /9-22 Q= - 1²³ 1²/³3 (№²=³² 0 0 0 Your answer (y - x) dx dy dz

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Q: dx Fa) Evaluate the integral z In(2x) using the substitution u = In(2.x). dx |r In(2ar) +C b)…

A: Topic = Integration

Q: 32. Find the integral: dx k² +1 (-1)*2 (k² +1) а. +C 5(-1)*2*k k? +1 k+1 b. +C (-1)*2* '(k +1)(k²…

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Q: Prove that m-l dx =0 m +n (し+x)" where m,n are both Positive

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Q: 2. (a) | +4 Evaluate the integral. √2x + 1 dx

A: Taking substitution as 2x+1 = t

Q: Derive a formula for In x dx where a. nt-1 b. n=-1

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Q: - 19 f(x+1)-(x2 - 6x +13) Ax + B √x²+bx+c² dx? (3)-In/x² - 6x + 13| + C The integral What is the…

A: Using partial fraction…

Q: 4 dx Vx(1 + x) roper for two reasons: The interval [0, co) is infinite and the integrand h 4 4 dx =…

A: Here we use substitution so simplify the integration.

Q: ull Pure Talk 12:55 PM 90% s3.us-east-1.amazonaws.com 1 | w(w2 + 1)³dw -1 x3 1 dx x2 sin30cos0 d0…

A: ∫-11ww2+13 dw=0, Since ww2+13 is odd.

Q: For x 1/2 dx and using the substitution u=x1/2, the resulting integral takes the form: 4u -du 4-12…

A: We can solve the integral by using substitution .

Q: dx 4. Evaluate the integral 0<a <1. 1+asinx

A: According to question,Given integral,∫02π dx1+a sin x,where,0&lt;a&lt;1

Q: ution 1- u? cos x and dx 1+ u? grand to a rational function of u, and t al. If you have a CAS, use…

A: We have to find the indefinite integral according to the given information

Q: 1. Evaluate the iterated integral: r12 Jo o cos(2) dy dx. -

A: To find ∫π2π∫0x21xcosyxdydx: First solve ∫0x21xcosyxdy: Let u=yx  dudy=1xdy=xdu…

Q: Q4) A) Find by using chain rule if f = ( , u=-1, x=-1 dx ++1 B) Evaluate the following integral: V2…

A: Given f(u)=u-1u+12   , u=1x2-1    , x=-1

Q: 1. Evaluate the given integral Q. -2 2y-2 -K² Q Jo 1 = (xy-1) dx dy

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Q: |1-y2 ху Q3. Evaluate the double integral dxdy /1– y²,

A: We have to find solutions

Q: B)Evaluate the integrals: i) √1-x2-x²-y² ii) -² ²-²-² dz dy dx. xe dy dx.

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Q: Evaluate the iterated integral. 2 3 4 (x² + y² + z² ) dx dy dz -2 0 0

A: ∫-22∫03∫04x2+y2+z2dxdydz

Q: a) Find the indefinite integral of the function 1 y = 3t2 + 2e3t +- + 2 cos 3t | b) Calculate the…

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Q: dx a) Evaluate the integral / z In(4x) using the substitution u = In(4x). dx x In(4x) +C b) Evaluate…

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Q: 39.: * Compute the integral: x (Inx) dx. a. (5e –1) b. (3e -1) c. (e +2) d. (5e -e') (e* -e) 32 16…

A: Use by parts integration

Q: 15. Evaluate the integral: sinz' dx А. 2л сos л? + с С. 1+ С В. xsinл* + С D. 0+C

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Q: Q3/ a) find the integral f 2* * cos2* dx dx b) the integral J e2x+1

A: Explanation of the answer is as follows

Q: Find the value of the improper integral or state that it is divergent. (If it is divergent, enter…

A: We will calculate the definite integral using basic definite integral properties and if we get an…

Q: iii. Find the particular integral (P.I) of y" + 9y = cos 3x

A: To find the particular integral P.I of  y''+9y=cos 3x

Q: The expanded form of the differential operator D(xD -1) is A xD +1 O xD? -D © xD? -1 (D) O xD?

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Q: What is the general solution to the DE, !! dt 2? - 2x + 2? What is the general solution to th O In…

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Q: dx 41. The following integral . (2x- 4) is improper

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Q: 3. Find the integral * dx a² -2 x+1 a.-x - - x - In(x + 1) + C 2 b.x2 – x – In(x + 1) + C c.x2 – x +…

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Q: 2. Calculate the following transcendental integrals: a) S² exee* dx X b) S (x²+1)In (x²+1) dx cos…

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Q: d.x (a) Evaluate the integral ; x In(4x) using the substitution u = In(4x). dx J r In(4x) +C -7x (b)…

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Q: 1-8 Evaluate the iterated integral. 1. 1 *y* dy dx

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Q: The integral of the given function | 4sinxcos G) dx is equal –3 cos () – 6cos () А. + C 2 3 cos ()…

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Q: Q.1) Evaluate the following integral ez dx (2e2 – 4e* – 1) - -

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Q: RA Find dx dt x In(x) /1 + (In(x))²

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Q: 1) Evaluate the triple integral. II x2 + y2 dV E E lies in x? + y² = 16 and between z = -5 and z =…

A: Given,  ∫∫∫x2+y2 dV   EE lies in x2+y2=16 and in between z=-5 and z=4

Q: Approximate the integral 1.6 2メ dx x²_4 using the Trapezoidal rule A -0.9 8EEEEE b' - -0.8 0.8666667…

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Q: Step by step

A: To evaluate the below indefinite integral