dx using miscellaneous substitution will yield to secx + 1 nsforming - S 1+2 / dz √²-22² dz 1+z² 1-z² -22 -dz -dz

Q: If a horizontal element is used to find the area bounded by y=√x, x=4 and the x-axis, the limits of…

A: Integration

Q: 9. For what value of k, k> 0, does (4kx-5k) dx = k² O 1 O 2 3 O 4

A: On solving this we will get

Q: Evaluate the integral: Se³+ A B C 3+cosh2x33+cosh2x sinh2x dx (3e)3+cosh2x + C 2+2ln3 (3e)3+ sinh2x…

A:

Q: Determine the area bounded by the functions f(x) = (x + 1)³ and g(x)= x + 1 3 A -unit² ® -/- unit² B…

A:

Q: In the indefinite Integral in(cosh x + e*)- A sinh xte cosh x + ex sinh x + ex In(cosh x + e*)…

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: 1 X + X Solve the integral: Gin|5+x²|+C A 5 @ B {/in/1+x³²|+c C © =√³ m/₁ + x ²³ / + C 6 ©…

A:

Q: Stretching spring: Eighteen pounds of force is required to stretch a spring 3 ft. from its natural…

A:

Q: Determine the integral: x²cosxdx A x²sinx + 2xcosx-2sinx + C B x²sinx-2xcosx-2sinx + C C…

A: integration

Q: Question 7 Evaluate: A B с dx (x+1) log(x+1) In 10 In [log(x+1)] + C 1 -In[log(x+1)] +C In 10 -log²…

A:

Q: The improper integral A e B 0 C D) 1 + ∞ [** 0 e-x dx is

A: The given improper integral is: I=∫0+∞e-xdx

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

A:

Q: ion 8 apply General Power Formula of Integration on which of the following sinhucothudu cosha coshu…

A: We have to choose the correct option from the given options

Q: sinh xte cosh x + e* In the indefinite Integral in(cosh x + e*)- (A) sinh x + ex sinh x tế B cosh x…

A:

Q: Evaluate the double integral: A) 40 B) 60 C30 D) 80 ²² (3x² +9y²)dxdy

A:

Q: Question 23 en [ "_f(x)dx=0 and ["f(x)dx = 1, evaluate Given A 0 B (u) D 11 76 55 =¹3f(x) dx -…

A: We have to find out the integral

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

A: Given that g(x) is a differentiable function and range of g(x) is interval I. f(x) is a function…

Q: If a horizontal element is used to find the area bounded by y=√x, x=4 and the x-axis, the limits of…

A: Horizontal element

Q: Evaluate the integral: e³+ cosh2x33+ cosh2xsinh2x dx 3+ (3e)3 + cosh2x A + C 2+2ln3 (3e)3 + sinh2x…

A: The integration are

Q: A solid is formed by rotating the area between the curves y = x and y = x² between x = 0 and x = 1…

A: To solve this problem we use washer method.

Q: Evaluate the improper integral 3 -2 X -dx

A:

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: 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: Determine the area bounded by the functions f(x) = (x + 1)³ and g(x) = x + 1. A unit² 3 B -unit² ©…

A:

Q: Evaluate the triple integral: A) 6 B) 18 C) 24 D) 12 3 2 1 ²³√ [²√ √ 0 (x+y+z)dydxdz

A:

Q: Evaluate the definite integral by substitution: 21 1 dx 3/(1+3r)² (1) ² 3/1 + 13xdx 10 (3) [TV. (3)…

A:

Q: 9 Let the integral be solvable' using trigonometric substitution. What is the correct choice of u…

A: A detailed solution is given below.

Q: If 8(x) = [e²-m (21+ - dx S[e²-In (21+1) ]dt, find g(x). -2 A e-In(2x+1) 4 B (2x + 1)² 2 Ⓒ (2x + 1)²…

A:

Q: √ Given A B CO f(x) dx = 0 and 11 55 6 √ √²+ f(x) dx = 1/201₁ 11 6 , evaluate √3 3f(x) dx - ₁2 f(x)…

A: To solve the integration using properties and given data.

Q: Given A (В B [²₁f(x) dx = 0 and 11 6 11 5 55 6 √ √ ² f(x) dx = 11 6 0 evaluate 0 [²3f(x) dx - ₁2f(x)…

A:

Q: Evaluate the double integral: A 9 2 5 2 (В с D m|w 416 5² 5²² 2ydydx

A: A detailed solution is given below.

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

A: Given g is a differentiable function and range of g is on the interval I and  F is antiderivative of…

Q: How many antiderivatives does a function of the form f(x) = x^ have when n=0? A may vary depending…

A:

Q: Evaluate the integral: 2 sin(3x)cos(3x)dx A B 1 4/6 —— 1 wlr 3 1 - wlw

A:

Q: wen 1₁² / 0x хо A) (-∞0,00) B (1,00) C{0,1} D) (-∞,1] -dx, determine all value/values of P for which…

A: Here  , we have two cases when p=1 and when p not equal to 1.

Q: Question 10 tanx If f(x)= A (B) C D sec ³x Itelin sec²x Iteline 1+1² I+e' -dt, then f'(x) equals…

A:

Q: Solve the integral: Seln(2x²+3x-4)³ (4x+3) dx (2x²+3x+4)¹4(4) A + C 3 eln(2x²+3x-4)³ B + C…

A:

Q: If f (x) = A) B (C) D tanx √1+1² 1+e' 0 1+tan²x tanx 1+e sec ³x -dt, then f'(x) equals tanx 1 + e In…

A:

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

A: Given that g be a differentiable function and the range of g be an interval I.  f is a function…

Q: Stretching spring: Eighteen pounds of force is required to stretch a spring 3 ft. from its natural…

A:

Q: Evaluate the improper integral (A) diverges (в B (C) ml+ 2 3 √√2²233/3dx 4

A:

Q: Evaluate the improper integral (A) diverges B (Q) Na O ساح 3 1²23 -dx

A:

Q: Evaluating √9-x² dx using trigonometric substitution will lead to: -3 C=/2 A 18 cos²0d0 (B) 1852/200…

A: See the details solution in below

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

A: We have to choose correct option

Q: Find the volume of solid generated by revolving the region bounded by g(x)=x²+2x+ 5about the x-axis.…

A: Given:      fx=x2+1      gx=-x2+2x+5  Volume of solid revolving around the region is…

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

A:

Q: tanx f f(x) = = [tion. A B C √1+1² 1+e' In (secx)√1+tan²x tanx 1+e sec²x 1+ e tanx sec ³x tanx 1+e…

A: Integration

Q: In S₁² = 10 A (1,00) B (-∞0,00) c) (-∞,1] D {0,1} Given -dx, determine all value/values of P for…

A:

Q: Evaluate the double integral: A B C D m|m NIG 2 2ydydx

A: You must have an idea of double integration to solve this problem. Option D is the right choice. The…

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

A: To solve this problem we use cylindrical shell.. method.