Given the integral secº (x - 1) tan* (x − 1)dx, which of the following equations will be useful for evaluation? 1 + cos2u A cos²u= 2 B sec²u = 1+tan²u 1- cos2u с sin²u= 2 D csc²u = cot²u+1

Q: Evaluating √9-x² dx using trigonometric substitution will lead to: -3 A 355/20 cos²0de 0 **/2 B Ⓒ 18…

A: Evaluate using trigonometric substitution ∫-339-x2dx=?

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

A: Here is the solution of the given problem. We solve this by using shell method

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

A: The integration are

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

A:

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…

A:

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

A: Volume

Q: tanx f f(x) = = [tion. A B C √1+1² 1+e' In (secx)√1+tan²x tanx 1+e sec²x 1+ e tanx sec ³x tanx 1+e…

A: Integration

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

A: We have to choose correct option

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

A: The integration are

Q: Evaluate the improper integral 3 -2 X -dx

A:

Q: Determine the area bounded by the curves x³ - y = 0 and y + 3x² − 4 = 0, using a vertical element.…

A:

Q: Let f(x)=√√√3x-2 on the interval √[²/3, ¹1] y=1 and y-axis about the y-axis and find the volume of…

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

A:

Q: . The daily amount of smog produced by cars coming into a city is given by y = 2 + 0.01x3/2, where y…

A:

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: + 1) dx A B C (x + 2) (x - 1)² = √ [++^2 + == 1 + (0-12 dc. ]dx. dx, the values of A & C…

A:

Q: Use the formula for the sum of the first n terms of a geometric sequence to find the sum of the…

A: Given that the geometric sequence is 7,14,28,56,112,....

Q: Evaluate the double integral: (3x2² +9y²) dxdy (A) 80 B) 40 Ⓒ30 (D) 60

A: To evaluate the double integral: ∫02∫0y3x2+9y2dx dy

Q: D sec²u=1+tan²u

A:

Q: Question 19 9 Let the integral be 'solvable' using trigonometric substitution. What is the correct…

A:

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

A: Correct option is A

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

A: Always false

Q: Which of the following can be determined given (A) L²³ F(x (f(x) + g(x) +h(x))dx g(x) dx © L² F…

A: We can solve this as follows:

Q: d If g (x) =-=-^[e'- In(2t+1)]dt, find g''(x) . dx -2 A ex-In(2x+1) 4 B et + (2x + 1)2 4 (2x+1)2² 2…

A:

Q: dx (x+1) log(x+ ) In[log(x+1)] + og² (x+1) + C

A: We have to choose the correct option from the given options

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

A:

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

A:

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

A:

Q: the indefinite Integral In(cosh x + ex)- A In(cosh x +ex) Sinh x + e* cosh x + ex (В sinh xtex sinh…

A:

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

A: A option is correct.

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: A lighthouse is on an island 400 meters off shore. The lighthouse beam makes a full turn every 15…

A: answer is in next step

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

A: Washer method

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

A: Now,The graph of the area bounded by f(x)=ex, g(x)=e-x and x=3 is shown below:

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

A:

Q: dx S secx + 1 1+z² Ⓒ √ 1+ 2²/ dz S A 1-z² -z² B 1+z² © √²/²+²/d² S³ -dz 1-z² 2-2z² / 1²= D 1+z²…

A: Note: According to our expert guidelines only first individual question is to be answered kindly…

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

A:

Q: If f (x) = A) B (C) D tanx √1+1² 1+e' 0 1+tan²x tanx 1+e sec ³x -dt, then f'(x) equals tanx 1 + e In…

A:

Q: s (x+1) log(x+1)

A:

Q: sinh xte cosh x + ndefinite Integral Sin(cosh x + e*)- In(cosh x + e*) sinh x te cosh x + ex

A: We have to calculate the given indefinite integral according to the given information

Q: luating√√9-x² dx using trigonometric substitution will lead to: **/2 sin²0d0 3 of th 9[*/ cos²0de…

A:

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

A:

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

A:

Q: To evaluate the integral 1 sin20 A sin cose= 2 1-cos20 B sin²0= 2 1 + cos20 (c) cos²0=- 2…

A: In this question, we want to know which identify is useful to solve the Integral.

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

A: We need to find volume.

Q: Determine the area bounded by f(x)=x²-x and x-axis. 2 A 3/3/14 unit² ® 1/1/¹4 B unit² 1 (C) unit² D…

A: The area bounded by fx=x2-x and x-axis

Q: Solve the integral: Seln(2x²+3x-4)²³ (4x + 3) dx (2x²+3x+4)4 (A) + C 4 B eln(2x²+3x-4)³ (4x+3)…

A: To solve the integral.