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

Q: Which of the following is a third degree partial differential equation? 3 дz J2z A др (В D др2 дz др…

A: given data  to find the degree of the partial differential equation

Q: feschucoshudu cschusinhudu sinhucothudu cosh coshu sinhudu O fir

A:

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

A:

Q: To evaluate the integral sin³0 cosed by trigonometric transformation, we use the identity;

A: Correct Option is D

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

A:

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 1 Evaluate:…

A: To solve the following problem

Q: Use summation notation to write the series -1+2+5+8+11...for 10 terms, then evaluate the sum.

A:

Q: Given [ f(x) dx = 0 and 11 0 11 6 55 6 rwax = 11 6 " evaluate S злах-п -1 2f(x)dx

A: Given,∫-11f(x)dx=0,∫01f(x)dx=116,To find ∫013f(x)dx-∫-102f(x)dx

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

A:

Q: 2. Find the area under the curve y = x² from x = 0 to x = 3. -y-x² (1,1) x-1 (3,9) x-3

A: Solved below.

Q: Solve the integral: A 6√√x +C B + C C D 37 6 3√√√x² √√√3/X 1x|m √x + C dx

A:

Q: =√x, x=4 and the x-axis, the limits of integration are: If a horizontal element is used to find the…

A:

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

A: D is correct option.

Q: Let f(x)=√3x-2 on the interval volume of the resulting solid. 83л (A - unit 3 135 83л (в -unit 3 125…

A: Region to be

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

A: Given,∫ x2cosxdx

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

A:

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

A:

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

A: We have to choose correct option

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: Find the are bounded by the curve y = x and y = x^2 - 2. * 2/9 sq unit 9/2 sq. units 16/3 sq. units…

A: Use the intersection of the curve and then integrate the upper curve minuses the lower curve to find…

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

A:

Q: If g (x) = — _ _[e¹ — ln(2t+1)]dt, find g''(x) dx -2 (A) B C) D 4 et + (2x + 1)2 4 et + (2x+1)2 e* -…

A:

Q: If f(x) = A B C -S sec²x D tanx l+et sec 3x √1+1² 1+e' 1+e lanx -dt, then f'(x) equals tanx 1+e In…

A: A detailed solution is given below.

Q: x+2 Determine the case of the following proper rational function after simplification: (x2 -…

A: Here, the rational function is: x+2(x2-4)(x3-8)=x+2(x2-22)(x3-23)=x+2(x-2)(x+2)(x-2)(x2+2x+4)

Q: Question 32 Solve the integral: A) 3√√√x² +C (B) ex 3 2√x² +C с D 6√√x +C 3√x x² dx

A:

Q: dx Transforming - using miscellaneous substitution will yield to secx + 1 (A) S= -dz 1+z² ® √ ²²+2…

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: Evaluate the improper integral A 0 B 2 (C) с D) diverges 3 4 12330² dx

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: Initially 73 grams of radioactive substance was present. After 3 hours the mass had decreased by 6%.…

A:

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

A:

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

A: Evaluate ∫dxx+1logx+1

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

A: Please follow the next step.

Q: Determine the area bounded by the functions f(x) = (x+1)³ and g(x)=x+1. 1 A unit² ® 2-unit² B 1…

A: Please see the below picture for detailed solution.

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

A: Application of integration

Q: the equation of the tangent line to the curve y = 4 sin x at the point equation of this tangent line…

A: We are asked to find the tangent line of the curve.

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: 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: For the given cost function C(x) = 72900 + 800x + x², First, find the average cost function. Use it…

A:

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

A:

Q: 25

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

A:

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

A: On solving this we will get

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

A: To evaluate the integral. Option A is correct.

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

A: Here we have to find the integral for finding the volume.

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: In the indefinite Integral Sin(cosh x + ex)- integrand? A In(cosh x + ex) B sinh x + ex In(cosh x +…

A: The given function whose integral is to be found is called the integrand.

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

A: To find y':

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

A: