1. Find the area of the region that lies inside the cardioid r = 1+ sin and outside the circle r = 1.

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

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Q: 46x Evaluate dx 2 Use rationalizing substitution. (A) none of the choices Be (ex - 2)1/² - √8 Arctan…

A: Let's find integration of given function.

Q: Which of the following can be determined given .3 3 3 [ f(x)dx = 5, ³g(x) dx = 7, and g(x) dx = 7,…

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Q: Which of the following can be determined given 3 A (f(x) = g(x)) dx 3 B [² (4f(x) +9h(x))dx с g(x)…

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

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Q: To reduce the DE (x+2y-4)dx-(2x+y-5)dy=0 to a DE with homogeneous coefficients, use the…

A: solution:-x+2y-4dx-2x+y-5dy=0dydx=x+2y-42x+y-5the system of linear equation…

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

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Q: Which of the following can be determined given A [²(f(x) + g(x) + h(x) dx 4 ® B √g(x) dx © (4f(x) +…

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Q: y = Arctan (2x)

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Q: Question 21 dx Evaluate: S (x+1) log(x+1) (A) In 10 log² (x + 1) + C 2 B In[log(x+1)] +C In 10 C…

A: We need to evaluate integral.

Q: That statement "We can use the General Power Formula of Integration for indefinite integrals…

A: Find:when we can use power formula

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

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Q: S Given dx, determine all value/values of P for which the improper inte хр A (-∞,1] B {0,1} C…

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Q: Determine the area bounded by the functions f(x) = (x + 1)³ and g(x)=x+1₁ unit² ® -unit² Ⓒ unit² 3…

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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: Determine the case of the following proper rational function after simplification: x + 2…

A: We have to find out simplification

Q: A freshly brewed cup of coffee has temperature 95°C in a 20°C room. When its temperature is 73°C, it…

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Q: Find the area bounded by x² = 4y + 4 and x = y - 2. Using vertical element, what is the integral…

A: The area bounded by the curves x2=4y+4 & x=y-2 is:

Q: Using the method of variation of parameters, the form of a particular solution pof (D²+25)y=4x²-3e5x…

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

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

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Q: V = 8TT². Which is the correct expression for dV dr dh 16ПР- dt dt dV dr = 16Tr dt dt dV = dt dV dr…

A: Topic:- application of derivatives

Q: Question 10 Let f(x)=√3x-2 on the interval volume of the resulting solid. 43x 135 83m 125 83x 135…

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Q: Solve the integral: √√ 3√x dx x²

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Q: Initially 80 grams of radioactive substance was present. After 4 hours the mass had decreased by 6%.…

A: Let's find amount remaining after 40 hours.

Q: Evaluating ³√9-x² dx using trigonometric substitution will lead to: 15/2 A cos²0d0 B 18 cos²0d0…

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

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

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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: A tank contains 50-liters of brine in which 20 grams of salt is dissolved. Pure water is being…

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

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Q: Question 27 9 Let the integral be 'solvable' using trigonometric substitution. What is the correct…

A: A detailed solution is given below.

Q: The general solution of the equation (D4 +D²)y= -12 is Ay=C₁ + c₂x + c3cOSX + csinx - 6x² B y=C₁ +…

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Q: dx Transforming secx + 1 2-2z² A 1+z² ® √ ₁ + 2²/1d² +z² B -dz 1-z² z²+z C / 1-z² Ⓒ / 1-²/²0 D 1+z²…

A: To find the transformation of the integral ∫dxsec x+1 after using miscellaneous substitution.

Q: (x+1)dx (x+2)(x-1)² S A 2 - x+2 B -1 + (x-1)2 ]dx. the values of A & C respectively are:

A: integration

Q: (x+1)x (x+2)(x-1)² If f @ 1/1 1/1/0 93 B C D 9 . - 2 3 2 9 3 - 2/3 . 93 A B 421 + + x+2 C (5-131].…

A: Explained below

Q: S √√9-x² dx using trigonometric substitution will lead to: **/2 cos²0d0 Evaluating Ⓒ 18/² A 95*1/2 B…

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

A: This question can be solved using integration by substitution.

Q: In evaluating S dx is same as evaluating lim C-3+ (In(f(x))). Determine the value of f(x) if x=3.4.

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

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Q: Given A B 1 -dx, determine all value/values of P for which the improper integral converges? to…

A: Using p-test form infinite limit we know that:  For a>0: If p>1 then ∫a∞1xpdx converges. Here…

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

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Q: Which of the following CANNOT be solved by method of undetermined coefficients? 1 A (D²+1)y=. cos x…

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

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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…

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Q: The function is x % = y? What is 8 2 dude Y æ2

A: We need to find derivative.

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

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