Given the integral sec (x - 1) tanª (x - 1)dx, which of the following equations will be useful for evaluation? A sin²u=- 1-cos2u 2 B cos²u= 1+ cos2u 2 csc²u= cot²u+1 sec²u=1+tan²u

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…

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Q: Evaluate the iterated integral. r4y *x + y [IT*** 6xy dz dx dy

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Q: Evaluate the double integral: A 40 B 80 C 60 30 ²(3x² +9y²) dxdy

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Q: Evaluate the improper integral 3 A 4 B O diverges N|9 름 12²233/30 dx

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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: 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: The gradient at any point (x, y) of a curve is given by dy-3x² +ax-36 where a is a constant. The…

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Q: 17. Evaluate [9e³x dx O9e³c+1 3c+1 O9e3c O9ec-3 3e³c-3

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

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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) +…

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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: Question 12 We can apply General Power Formula of Integration on which of the following integrals? A…

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

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Q: Fiind a33 of an arithmetic sequence if the common difference is -1 and a1=3

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

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

A: g(x) is integrated in the interval 0 to 3 f(x) and h(x) are integrated in the interval 0 to 3

Q: 15+0. The improper integral e* dx is

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Q: Question 11 puas √1+1² Ffxx)=f -dt, then f'(x) equals 0 I+e' In(secx)√1+tan²x Itela tanx sec³x 1+ele…

A: Topic:- application of integration  Note :- as per our guideline if more than one question uploaded…

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

A: Substitute sec^2u=1+tan^2u B option is correct.

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

A: topic- indefinite integral

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

A: Please see the below picture for detailed solution.

Q: How many antiderivatives does a function of the form f(x)=x" have when n*O₂ A infinitely many B may…

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

A: The first problem is related to simplification and second one is related to linear composition.

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

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Q: dx secx + 1 Transforming - -z² A 1+z² B z²+z 1-z² 1+z² Ⓒ 1- D √ -dz -dz -dz - 2z² 1+z² -dz using…

A: Here, the given integral is: I=∫dxsec…

Q: Determine the integral: [x²cosxdx

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

A: find out the work required fo stretch the spring an additional 3 ft.

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

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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: Evaluate the double integral: (A) 40 B 30 C) 60 D) 80 ²(3x² +9y²) dxdy

A: The integration are.  .

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

A: consider9x2+6x-7=9x2+6x+9-16=9(x+3)2-16 let u=x+3⇒du=dxThen9(x+3)2-16=9u2-16

Q: (x-1)dx x(x²+1)(x² +2) S=

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

A: The integration are

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: If f(x) = A B (C) tanx S 0 sec ³x 1+e tanx 1+tan²x 1+ e tanx 1+12 sec²x 1+e tanx In (coor) 1+ e'…

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

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Q: If f(x) = A B C D tanx S 0 sec²x √1+1² 1+e¹ -dt, then f'(x) equals 1+e tanx In (secx)√1+tan²x 1+ e…

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Q: S sec (x-1) tan4 (x - 1)dx, which of the following equations will be useful for 1 + cos2u cos²u= 2…

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Q: Question 2 Solve the integral: A √√x 3 B 33√/ x² +C 3√x² +C 6 6√√x +C D √√ 3√x dx

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

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Q: Solve the int B ²+3x-4)³ (4x+3)dx integral: Seln (2x² + 3 eln(2x²+3x-4)³ + C (2x²+3x-4) (-4)³² (4x +…

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

A: Option C is correct option

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

A: Option (B) is the correct answer.

Q: q13

A: We have to calculate the given indefinite integral

Q: Question 4 Which of the following is NOT a method for finding volume of solids of revolution? A…

A: Please see the below picture for detailed solution.

Q: COS (+3 O cos x Ocos 2x O sin a Ocos z +x) + cos (-) is equivalent to:

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

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Q: . Evaluate 1 4-x² dx

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