3+ Evaluate the integral: e³+ cosh2x33+ cosh2xsinh2x dx (3e)3+ sinh2x A +C 2+In3 (3e)3 + cosh2x +C 2+2ln3 (3e)3+ sinh2x 21n3 (3e)3 + cosh2x 21n3 (В + C +C

Q: 17. Evaluate [9e³x dx O9e³c+1 3c+1 O9e3c O9ec-3 3e³c-3

A:

Q: Evaluate the improper integral A 0 (B 4 C diverges 2 D 9 mit 2 3 -2 X 3 dx

A:

Q: If g(x) = d __*[e' - In(2t+1)]dt, find g''(x) . dx -2

A:

Q: Evaluate the triple integral: A 24 B 6 12 18 √₁³√₁² √²(x + y + (x+y+z)dydxdz

A:

Q: Find the area bounded by : f(x)=e*, g(x)=e* and x=3.

A:

Q: Evaluate the integral: Sen(1²2+3x-7) е dx A x² + 5x+In 3x-6|+C XZ B +5x+31n|x-2|+C 2 C x ²2+ = +…

A: On solving this we will get

Q: (x+1) dx (x+2)(x-1)² 2 3 If 15 S. A B (C) D -10 2 . 9 3 W|N I 93 9 —— 3 =1[₂ = A x + + B x-1 +…

A:

Q: 1 S dx 3 x + x Solve the integral: 5 A + x +C 1+x+c n 1+x+c in 1 B + x + C © 6/5+x²³/+c C ® 1+x+c In…

A:

Q: Find the area bounded by : f(x)=e*, g(x)=e¯* and x = 3. A (e²+ 1)² e² sq. units B (e³-1)² e3 (e²-1)²…

A:

Q: Question 11 Let g be a differentiable function, and let the range of g be an interval 1. Suppose…

A: The integration are...

Q: dx Transforming - using miscellaneous substitution will yield to secx + 1 A -dz 1+z² B 1² 2-2z² 1+z²…

A: Given problem:-

Q: dx secx + 1 Transforming S Ⓒ 1 +²2² A 1-z² (В) / z²+z 1-z² 2-2z² © 1+z² -z² Ⓒ S 1=32/2/dz D 1+z² -dz…

A: Solve using miscellaneous substitution

Q: √ √9-x S*/2 (B 9 ft/cos Ⓒ 18 "/2 D 95*1/2 sin Evaluating A 18 9-x² dx using trigonometric…

A:

Q: X+2 Determine the case of the following proper rational function after simplification: (x²-4)(x³-8)…

A:

Q: f(x) and g(x) are integrable on the closed interval [a, b], and k is a constant, which of the…

A: We have to find out the solution

Q: dx Evaluate: (x+1) log(x+1) 1 A In10 log² (x+1)+C 2 B -log² (x + 1) + C 2 In 10 In[log(x+1)] + C…

A: We have to integrate of given function

Q: Which of the following can be determined given 3 A - (f(x) = g(x))dx B (4f(x) +9h(x))dx 3 © (f(x) +…

A: g(x) is integrated in the interval 0 to 3 f(x) and h(x) are integrated in the interval 0 to 3

Q: If f(x) = (A) B - St √1+1² 1+e' 0 In (secx) √ 1+tan²x tanx 1+e 1+tan²x tanx D tanx 1+e sec ³x 1+…

A:

Q: If f(x) and g(x) are integrable on the closed interval [a, b], and k is a constant, which of the…

A:

Q: Using shell method, find the volume of R, when it is bounded by y = x³, x = 0, y = 8 about x- axis.

A: Shell method

Q: dx ·S (x+1) log(x+1) Evaluate:

A: Given that,

Q: If a horizontal element is used to find the area bounded by y=√√x, x=4 and the x-axis, th (A) 0 and…

A: Topic:- application of integration

Q: Determine the area bounded by f(x) = x² − × a axis. A - unit² B unit² C unit² 2 -unit? +|5

A:

Q: Let g be a differentiable function, and let the range of g be an interval I. Suppose that f is a…

A: The correct answer is option (c).

Q: Solve

A: We have to calculate the given indefinite integral

Q: Question 36 Evaluate the triple integral: (x+y+z)dydxdz 0 A 24 B) 18 (C) 6 D) 12

A:

Q: d If g(x) = - S* [e'− ln(2t+1)]dt, find g''(x) dx -2 2 A ex. (2x + 1)² 4 (В B et + (2x + 1)² Ⓒe*…

A: Given that gx=ddx∫-2xet-ln2t+1dt

Q: Question 16 d If g(x) = == S[e²-In (21+1) ]dt, find g(x). dx 4 A et + (2x+1)2 e* -In(2x+1) 4 e¹+ (2x…

A: We will first find g(x).

Q: Evaluate the integral: A 16 밴 3 sin(3x)cos(3x)dx

A: ∫sin(3x)cos(3x)Substitute u=sin(3x)→dudx=3cos(3x)→dx=13cos(3x)du=13∫uduWe know that…

Q: We can apply General Power Formula of Integration on which of the following integrals? A Seschu…

A: We have to choose correct option

Q: Find the area bounded by : f(x)=e*, g(x) = e¯* and x = 3. A (e²-1)² e2 sq. units (e²+ 1)² e2 (e³-1)²…

A:

Q: To evaluate the integral sin ³0cos 0d0 by trigonometric transformation, we use the identity; A…

A: ∫sin3θcos6θ dθ

Q: y = x3 – x’cosx + 2xsinx +2cosxx

A:

Q: Determine the area bounded by f(x)=x²-x and x-axis. A unit² -unit2 unit² |+ B 2 © ½ u Ⓒ / unit ² D…

A: Let's find area of given curve.

Q: Given the integral sec (x - 1) tan4 (x - 1)dx, which of the following equations will be useful for…

A: Let's find useful formula for evaluation of integration.

Q: (a) Find the intervals on which f is increasing or decreasing. (b) Find the local maximum and…

A:

Q: Evaluate the triple integral: 3 2 1 S³ S² S²(x+y+z)dydxdz 0 A 12 B 18 C 6 D) 24

A:

Q: (x2y3 - 1+) dx + x3y2dy = 0 1+9x2

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Which of the following represents the volume of the solid generated by revolving the region bounded…

A:

Q: tanx If f(x) = (Α) B C D S 0 sec ³x 1+etanx In (secx) √ 1+tan²x tanx 1+e sec²x 1+ etanx 1+1² -dt,…

A: Here, given that: f(x)=∫0tan x1+t21+etdt...(1)

Q: Question 20 How many antiderivatives does a function of the form f(x)=x" have when n*0₂ (A) 1 (B)…

A: Antiderivative means Integration

Q: tanx -√ S sec²x 1+ et tanx In (secx) √✓ 1+tan²x 1+ elanx sec ³x 1+etanx If f(x) = A B (с 1+1² 1+e'…

A:

Q: S dx Evaluate: (x+1) log(x+1) 1 A ¹-In 10 log² (x + 1) + C 2 B In 10 In[log(x+1)] + C 1 C…

A: We will evaluate the given integral using simple Integration rules.

Q: Evaluate the improper integral 3 A 4 B) diverges с 0 D 2 N|O √√² 3³/3 m|f dx

A:

Q: solve the following differential eqaution : (2x+y)dx-(4x+2y-1)dy=0

A: Solved below.

Q: Let the integral be 'solvable' using trigonometric substitution. What is the correct choice of u…

A: We need to choose correct option.

Q: (x+1) dx (x+2)(x-1)² = √ [+²2 S₁ B + - - 1 + x-1 (x-1)2 ]dx. the values of A & C respectively are:

A:

Q: Let f(x)=√3x-2 on the interval. 1] Revolve the region between the curve, y=1 and y-axis about the…

A: Here is the solution of the given problem. We solve this by using shell method

Q: Evaluate the integral: sin(3x)cos(3 A - B C D H|ო 3 16 +16 dx

A:

Q: dx S secx + 1 1+z² Ⓒ √ 1+ 2²/ dz S A 1-z² -z² B 1+z² © √²/²+²/d² S³ -dz 1-z² 2-2z² / 1²= D 1+z²…

A: Note: According to our expert guidelines only first individual question is to be answered kindly…