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

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

A:

Q: Question 3 In the indefinite Integral in(cosh. x +ex). sinh x +e* (A cosh x + ex sinh x + ex In(cosh…

A: The integration are

Q: q13

A: We have to calculate the given indefinite integral

Q: Evaluate the triple integral: A) 12 B) 6 C) 24 D) 18 3 2 1 (x+y+z)dydxdz

A: We have to choose correct option

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

A: Find out the area bounded by curves.

Q: Given 1 [₁f(x) dx = 0 and -1 1 S²F(x f(x) dx = 11 6 I evaluate 1 √²3f 3f(x) dx - .0 -1 2f(x) dx.

A: Explained below

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: Please write out/show work, thank you! Find the slope of the line tangent to 2xy + π sin y = 2π…

A:

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

A:

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

A: Find:when we can use power formula

Q: Given the integral sec (x - 1) tan4 (x - 1)dx, which of the following equations will be useful for…

A: Let's find useful formula for evaluation of integration.

Q: πT Evaluate the integral: sin(3x)cos(3x) dx រ 1 A 3 (B) i D 1 براس 1

A:

Q: dx Transforming - using miscellaneous substitution will yield to secx + 1 A -dz 1+z² B 1² 2-2z² 1+z²…

A: Given problem:-

Q: sinh x + ex cosh x + ex In the indefinite Integral in(cosh x + ex)- dx, what is the integrand?

A: Intergrand

Q: d & fle²- · *[e' – In(2t+1)]dt, find g''(x) . dx -2 If g(x) = - A B c) e*- D 4 et + (2x + 1)² e* -…

A:

Q: 9 Let the integral be 'solvable' using trigonometric substitution. What is the correct choice of u…

A: We have to solve

Q: 5. (D²+4)y=4 cot 2x

A: We use variation of parameters method to solve the given differential equation.

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

A: We have to solve integral

Q: Evaluate the double integral: 4 LA LE 2ydydx

A:

Q: d If g (x) = ª[e' - In(21 + 1)]dt, find g(x) . dx A e-In(2x+1) 4 (В et + (2x + 1)² 2 (C) (2x + 1)² 4…

A: Topic:- application of integration

Q: feschucoshudu cschusinhudu sinhucothudu cosh coshu sinhudu O fir

A:

Q: Let f(x)=√√3x-2 on the interval volume of the resulting solid. 43л A -unit 3 125 43л B 135 83ñ 125…

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Q: (a) Find the intervals on which f is increasing or decreasing. (b) Find the local maximum and…

A:

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

A: Integration

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

A:

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

A:

Q: Determine the integral: x²cosxdx x²sinx + 2xcosx-2sinx + C B x²sinx-2xcosx-2sinx + C с…

A: Here we have to determine the given integral.

Q: Question 28 dx Evaluate: Tx (x+1)log(x+1) 1 A -log² (x+1)+C 2 1 ® --In 10 log² (x + 1) + C B 2 (C)…

A:

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

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Q: 14. Evaluate [4³x dx 3x O 4³x 3x +C 6ln2 O 4³x In4 O 43x+1 3x+1 +C O None of these +C

A:

Q: cylinder cone pyramid if this triangle is rotated about the x axis, what figure is formed?

A:

Q: How many antiderivatives does a function of the form f(x)=x" have when n*0= A) infinitely many (B)…

A: We have to choose option find antiderivative

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

A: To solve the integral.

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

A:

Q: $²² Α) (1,∞0) B (-∞,1] (-∞0,00) Given D {0,1} dx, determine all value/values of P for which the…

A:

Q: x²+3x-7 X-2 +5x+31n|x-2|+C + +In|3x-6|+C 2 x²+5x+In/3x-6|+C x² + 5x + n/x-21 +C 2 3 In Evaluate the…

A:

Q: w/N Let f(x)=√√3x-2 on the interval y-axis and find the volume of the resulting solid. Revolve the…

A: Application of integration

Q: Evaluate the improper integral A 0 (B 4 C diverges 2 D 9 mit 2 3 -2 X 3 dx

A:

Q: Question 14 If [ _ ( x + 1) dx S A B C D (x+2)(x-1)² 2 . 93 -io 1 6.11 1 -- - 9 9 2 - - 3 - 3 2 - 3…

A: To find the value of A and C  in the given integral.

Q: If f(x) = (A) B - St √1+1² 1+e' 0 In (secx) √ 1+tan²x tanx 1+e 1+tan²x tanx D tanx 1+e sec ³x 1+…

A:

Q: wen 1₁² / 0x хо A) (-∞0,00) B (1,00) C{0,1} D) (-∞,1] -dx, determine all value/values of P for which…

A: Here  , we have two cases when p=1 and when p not equal to 1.

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: Determine the area bounded by f(x)=x²-x and x-axis. A unit² (В B (c) unit² D unit² w|m 16 H|4 unit²

A: Given that we need to find the area bounded by f(x) = x2 -x  and x- axis.  Now,

Q: Evaluate the triple integral: (x+y+z)dydxdz A) 18 B) 24

A: ∫03∫02∫01(x+y+z)dydxdz=∫01(x+y+z)dy=xy+y22+zyUpon substituting=x+0.5+z-0=x+0.5+z

Q: tanx -√ S sec²x 1+ et tanx In (secx) √✓ 1+tan²x 1+ elanx sec ³x 1+etanx If f(x) = A B (с 1+1² 1+e'…

A:

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: 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 C…

A: To find the area bounded by curves

Q: If f(x) and g(x) are integrable on the closed interval [a, b], and k is a constant, which of the…

A: Definite integral Property : ∫ab fx±gx dx = ∫ab f(x) dx ± ∫ab g(x) dx. ∫ab k f(x)dx =k∫abf(x)dx ;…