Find the area bounded by x² = 4y + 4 and x = y - 2. Using vertical element, what is the integral equation to solve for the area? Ⓒ 1² ( ³ + x - 1 + x²) dx A ® √ ² ( x + 1 - - - ² ) d x B dx 4 © S² ( x + ² = x ² + + ) d² dx 4 Ⓒ √ ² ( ² + x - + -+²) 4² D dx E None of the choices

Q: Evaluate the double integral: 2 √ ² √² (3x² +9y²) dx dy 0

A: To solve the given double integral.

Q: Question 9 d If g(x) = ·S*^[e'− In(2t+1)]dt, find g''(x) . dx -2 4 A (2x + 1)2 4 B (2x + 1)²…

A: Using leibnitz rule.

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

A: Answer: A

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

A: The given expression is:…

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

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

A:

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

A: You must have idea of integration to solve it.

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

A:

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

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: Evaluate the given definite integral [ 2x³ – 6x² dx, from x = 1 to x = 2 X²

A:

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

A:

Q: Graph cach function using radians. 2. 1 - sin 29 - 1 2 0 0 0 یا

A: Please see the below picture for detailed solution.

Q: Which of these expressions represents the area bounded by y = 1/2 x^2 and y = 3x? * 6x + x²dx 6x…

A: To solve the following problem

Q: Determine the area bounded by the functions f(x) = (x + 1)³ and g(x)= x+1. 3 A unit² 3 Ⓒunt² unit² D…

A: topic- area bounded by curves

Q: X √√/31/22 Solve the integral: 3√/x² A + C 6 B 6√√√x + C C3√√√x² + C C) dx

A:

Q: Find the volume of the solid generated by revolving the given plane area having the given boundaries…

A:

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

A: A detailed solution is given below.

Q: -Je cosx dx

A:

Q: Determine the area bounded by f(x)=x²-x and x-axis. 1 (A) -unit² B -unit² © == unit² C Ⓒ / / unit² D…

A: Find out the area bounded by curves.

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

A: Given,∫ x2cosxdx

Q: We can apply General Power Formula of Integration on which of the following integrals? @ /. A coshu…

A: we have to find the integral by general power formula

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

A: Topic:- application of integration

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

A:

Q: Evaluate the triple integral: 3 ₂2 0 (x+y+z)dydxdz

A:

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

A: To solve the integral.

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

A: Correct option is missing

Q: 2x ind the derivative of: 2e cos(8x). [Hint: use product rule and chain rule!] se e^x for e*. ow,…

A:

Q: Which of the following can be determined given Ⓒ [² (4f(x) + 9h(x)) dx 3 ® √²³((x) + B © ²(f(x) -…

A:

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

A: Topic:- application of integration

Q: How many antiderivatives does a function of the form f(x) = x^ have when n0? (A) 1 B) none (C)…

A:

Q: Which integral below gives the volume of the solid of revolution obtained by rotating the bounded…

A:

Q: d If g(x)=- S* [e²-In (21+1) ]dt, find g(x). -2 2 (2x + 1)2 4 B (2x + 1)² Ⓒe-In(2x+1) 4 (2x + 1)² di…

A: We have to find out derivative

Q: Given the integral sec6 (x − 1) tan4 (x - 1)dx, which of the following equations will be useful for…

A: The given integral,       ∫sec6x-1tan4x-1dx

Q: Evaluate the double integral: A B C D m 100 +10 9|N NIG 4 S** 2ydydx 1

A: A detailed solution is given below.

Q: Determine the area bounded by the functions f(x) = (x + 1)³ and g(x)= x +1.

A: Correct option is A

Q: 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 option

Q: 1 √√√√√x+x X Solve the integral: S- @ =√² m/1 + x ²³ / + c A C (1) 6in/5+ x ³²³| +C B © ²/³ m/1 + x…

A:

Q: Question 15 Evaluate the double integral: (A) 40 B) 80 C) 60 (D) 30 ²² 6) (3x² +9y²) dxdy

A: we can find the double integral.

Q: S 1 Solve the integral: √√√X = n/1+x²³²|+c A C {/in/1+x²³ | +c B © 6n/5+x²³²|+c C in/1+x³| +c D X +…

A:

Q: Question 9 Which of the following represents the volume of the solid generated by revolving the…

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: dx using miscellaneous substitution will yield to secx + 1 Transforming 1+z² Ⓒ √ 1 + 2/²/d= (A) -dz…

A: First of all, note that sec x=tan2x2+11-tan2x2⇒sec x+1=tan2x2+11-tan2x2+1⇒sec…

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: 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: