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

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A: Using Leibnitz integral rule.

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A: Topic:- application of integration

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

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A:

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Q: + ∞o [** S The improper integral A B) 1 8 ex dx is

A: ∫0∞e-xdxSubstitute u=-x→dudx=-1→dx=-du=-∫euduWe know that ∫audu=auln(a)

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Q: Given A) B (C) D 11 √ √ ² f(x) dx = = /10 f(x) dx = 0 and 11 6 20 55 •[ 37/(x)dx - 5² 2/(x)dx…

A: D option is correct.

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A: Topic :- application of integration

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A: Solved below.

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Q: 1 Solve the integral: S dx 3 x ที่ X + X h_1+x+c A C Ⓡ 6ın|5+x=³² | +C B © h1+x8 l+c + C h1+x+c D +…

A: Given that we need to solve the following  integral.

Q: Find the area bounded by : f(x)=e*, g(x)=e* and x=3.

A:

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Q: tanx If f (x) = A (В) (ⒸC) D - St 0 sec 3x 1+ e tanx In (secx) √ 1+tan ²x 1+ e tanx sec²x 1+elanx…

A: Finding the derivative of the integral

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A: According to the properties of definite integral(A) ∫abkf(x)dx=k∫abf(x)dx      True(B)∫abkdx=k…

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Q: Which of the following can be determined given f(x)dx=5, g(x)dx=7, and and T h(x) dx = -5

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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

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

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Q: dx using miscellaneous substitution will yield to secx + 1 Transforming S Ⓒ √ ²² +²2 dz (Α) -z²…

A: This question can be solved by substituting z=tanx2

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

A: Volume

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

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

A: