In Exercises 5-16, apply Trigonometric Substitution to eval- uate the indefinite integrals. 5. [√x2² √x² + 1 dx

Q: What is the domain of sech-1 x? How is sech-1 x defined in terms of the inverse hyperbolic cosine?

A:

Q: Evaluate the integral | tan° 2x dx 5

A: Solve the given integral.

Q: Vcsc² 0 – 1d0 [In (sin 0)]² + 23

A:

Q: use Theorem to find 31) F(A) = 4t? 5 Sin 34

A: To find the Laplace transform of the below function using the theorem. ft=4t2−5sin3t

Q: Evaluate S₁ 45 dx 1- cos (9x)

A: To evaluate .

Q: Use trigonometric substitutions to evaluate the definite integral 1 [5x²³√1-x² dx.

A:

Q: How does the method of substitution work for definite integrals? Give examples.

A: To elaborate the use of substitution for computing the integrals with example.

Q: 3.) Evaluate the definite integral. Show your work. You may check your answer by using a calculator.…

A: Given expression ∫131+2x+3x2x2dx=? we know ∫xndx=xn+1n+1                  ∫1xdx=ln|x|

Q: Explain how the fundamental theorem of calculus relates integrals and derivatives. Formats T B T U…

A: Fundamental theorem of calculus relates integrals and derivatives.

Q: Solve the equation x + 2y = sin x when y(™) dx 1 ㅠ

A:

Q: Find the area given by: fin In(x)dx

A: Follow the procedure given below.