Stretching spring: Eighteen pounds of force is required to stretch a spring 3 ft. from its natural length. Find the work required to stretch the spring an additional 3 ft. A 33 foot-pounds (B) 24 foot-pounds 27 foot-pounds 30 foot-pounds D

Q: If f(x) = Α) B C D tanx sec ³x 1 + e tanx 1+tan²x 1+ e tanx sec²x 1+1² 1+e' -dt, then f'(x) equals…

A: We have to find derivative of given integral.

Q: I sin sin ³0cos Ode by trigonometric transformation, we use the identity; To evaluate the integral…

A: We have to slove integral

Q: Question 18 Evaluate the integral: e3+ cosh2x33+cosh2xsinh2x dx A (3e)3+ sinh2x 21n3 + C (3e)3+…

A:

Q: Question 31 Evaluate the integral: A B C D H|m 1 1 13 1|6 sin(3x)cos(3x) dx

A: To evaluate the integral.

Q: (D) 1

A:

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

A:

Q: Solve the integral: Seln(2x² + 3x−4)³ (4x + 3)dx

A:

Q: Which of these expressions represents the area between the curves y = x^2 and y = 6 - x from X = 0…

A:

Q: Determine the integral: x²cosxdx (Α x²sinx-2xcosx-2sinx + C x²sinx + 2xcosx+2sinx + C x²sinx-2xcosx…

A:

Q: Evaluate the triple integral: A) 18 B) 24 C) 12 D) 6 3 2 S²³² S²(x+y+z)dydxdz 0

A: We have to find the value of given integral

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

A:

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

A: Solved below.

Q: en 0 3 | f(x)dx=0 and. -1 S 11 11 5 55 6 f(x) dx = = 11 6 , evaluate 1 J 3f(x)dx - [2f(x)dx.

A: We will distribute the integral in two parts .

Q: Given √√2/10 dx, determine all value/values of P for which the improp хр onverges? A) {0,1} B)…

A: Topic:- application of integration

Q: The improper integral A 1 B 0 C St edx is

A: To solve the improper integration.

Q: Q/IF 3= sin(X) (²314) y = 3² sin(x) cos(x) Prove that

A: To find y':

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

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

Q: If f(x) = (A) B C D tanx sec ³x 1+e 1+1² 0 sec²x 1+ e tanx In (secx)√√ 1+tan²x tanx 1+e 1+tan²x 1+ e…

A:

Q: Evaluate the double integral: A) 80 B) 30 C 60 D 40 √²² (3x² +9y²) dxdy 0 0

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: x³√/x² + 1dx

A:

Q: ₁₁³f(x)dx=5₁ g(x)dx=7, and 5, Which of the following can be determined given A [ (4f(x) + 9h(x) dx ®…

A: See the details solution in below

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

A:

Q: Transforming S Ⓒ √ 2²-22²2 =2 A -dz 1+z² z²+z B -dz 1- © S с © S D N dx using miscellaneous…

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: According to the properties of definite integral(A) ∫abkf(x)dx=k∫abf(x)dx      True(B)∫abkdx=k…

Q: The improper integral A B if the 0 1 0 e dx is

A:

Q: Which of the following can be determined given f(x) dx = 5, g(x) dx = 7, and Sh(x) dx = -5 3 A √…

A:

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

A:

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

A:

Q: Which of the following can be determined given 3 3 3 [ f(x)dx=5₁ g(x)dx=7, and 1₁h(x) dx = -5 4 A…

A: Given the integral values of f(x) , g(x) , and h(x) on different intervals.  We need to check the…

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

A: Here we have to determine the given integral.

Q: Solve the integral: √x 3 / x2 + C 6 6/x + C 33.2 + A B (C) D + C dx

A: On solving this we will get Option (C) is correct

Q: 6. Find the area enclosed by the curve x² + 8y + 16 = 0 the x-axis, the y- axis and the x-4 = 0…

A:

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

A: To solve the integral.

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: Question 32 dx Evaluate: (x+1) log(x+1) A) -In 10 log2 (x+1) + C 2 B --log² (x+1)+C 2 In 10…

A:

Q: Find the volume of solid generated by revolving the region bounded by f(x)= x² + 1and…

A: Volume

Q: Determine the area bounded by the functions f(x) = (x + 1)³ and g(x)=x+1₁ 1 A -unit² (B) unit² 1 H|m

A: Given that fx=x+13  and gx=x+1Solution :x+13=x+1x+13-x+1=0x+1x+12-1=0x+1=0 and x+12-1=0x=-1 and…

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

A:

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

A:

Q: The improper integral (A) e B) 0 с 00 D 1 8 0 edx

A: ∫0∞e-xdxSubstitute u=-x→dudx=-1→du=-dx=∫-e-x

Q: Which of the following can be determined given f(x)dx=5, g(x)dx=7, and h(x)dx= -5 Ⓒ [²(f(x) + g(x) +…

A: Give∫13 f(x) dx = 5, ∫03g(x)dx=7, and ∫13h(x) dx = -5

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

A:

Q: Evaluate the integral: e3+cosh2x33+cosh2xsinh2x dx (Α) (3e)3+ sinh2x 2+In3 + C (3e)3+cosh2x B 2+2ln3…

A:

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

A:

Q: tank has pure water flowing into It at 10 L/ min. The contents of the tank are kept thoroughly…

A:

Q: Find the volume of solid generated by revolving the region bounded by f(x) = x² + 1and g(x)=x²+2x+…

A: The volume of the solid is 63π unit3

Q: $²² Α) (1,∞0) B (-∞,1] (-∞0,00) Given D {0,1} dx, determine all value/values of P for which the…

A:

Q: To evaluate the integral sin³0cos0de by trigonometric transformation, we use the identity; A sin²0=…

A:

Q: B S₁ Evaluate: A In 10 (В) ® -log² (x+1)+C 2 In 10 In[log(x+1)] + C -In 10 log2 (x+1)+C 2 D dx (x+1)…

A: