Find the volume of solid generated by revolving the region bounded by f(x) = x² + 1and g(x)= x² + 2x + 5about the x-axis. A 72x unit ³ (B) 63л unit 3 Ⓒ37x unit ³ (D 56 unit ³

Q: If f(x) = A B D tanx S™ 0 1+tan²x 1+etanx sec ³x l+etanx In (secx)√1+tan²x 1+etanx sec²x tanx 1+12…

A: Using the Leibnitz rule:

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

A: Please see the below picture for detailed solution.

Q: Transforming A B C D dx using miscellaneous substitution will yield to secx + 1 2-2z² -dz 1+z² z²+z…

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

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

A: What is the integrand

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: In the indefinite Integral in(cosh x + e*). sinh x + ex cosh x + ex dx, what is the integrand?

A:

Q: the work required to stretch the spring an additional 3 ft. 24 foot-pounds 33 foot-pounds 30…

A: Topic :- calculus

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: 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

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A:

Q: Question 37 1 Solve the integral: S- dx √√√√x+x A m/1+ + X +C ℗ 6n/5+x²³| +C B Ⓒ1+x²+c с X C =…

A:

Q: The orthogonal trajectories of the family of curves y = cx² is A x=ky² B C x²+2y²=k 2x² + y² = k

A: We have to find the

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: 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: 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 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: d If g(x)=- -S*[e' - In (21+1)]dt, find g(x) Se dx 4 A (2x+1)² 4 B e+ (2x + 1)² Ⓒe* -In (2x+1) 2 D…

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: B option is correct.

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: 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: Evaluate the improper integral 3 A 4 B) diverges C D —— 6/0 m|+ ² 0

A: Topic:- application of integration

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

A:

Q: If a horizontal element is used to find the area bounded by y=√√x, x=4 and the x-axis, th (A) 0 and…

A: Topic:- application of integration

Q: x³√/x² + 1dx

A:

Q: Determine the area bounded by f(x)=x²-x and x-axis. 1 A unit² 2 Ⓡuni B 1 Ⓒ / unit² Ⓒ / unit² -unit²

A:

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: 2) Find the standard deviation of the population sample. 2, 4, 7, 12, 15 3) Find the variance for…

A:

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

A:

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

A:

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

A:

Q: Let f(x)=√3x-2 the y-axis and find the volume of the resulting solid. 83 (A) -unit ³ 135 83 (B)…

A: We will draw the curve f(x) and y=1. Points of intersectionf(x)=3x-2   and y=11=3x-2 1=3x-2x=1Point…

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

A:

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

A:

Q: 25

A:

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

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: C option is false

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

A:

Q: √__(x+1) dx (x+2)(x-1)² 1 9 3 2 0-11/11 - 01/17 9 3 2 3 1 2 9 3 -io 1 9 - = 1[ A B + x+2 x-1 + C…

A:

Q: Evaluate the double integral: 2ydydx A 4 9 B) m 100 8 NIG 2 9 2

A: To find the value of given double integral.

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: 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: Determine the area bounded by f(x)=x²-x and x-axis. unit² B unit² Ⓒunt² D unit²

A:

Q: (D) 1

A:

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

A:

Q: Determine the derivative of the following algebraic and non-algebraic functions. 1. f(x) = sinx +…

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Q: The improper integral A 0 B 1 с e D 8 +∞ St 0 ex dx is

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Q: a + bx² 3ax + bx³ dx

A:

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…

A:

Q: (x + 1) dx (x+2)(x-1)² 15 S= = √ [ +42 A B + x + 2 x-1 C + + (x-1)2]dx. dx, the values of A & C…

A: