10. (a) Consider the integral dx. x² Why can't this integral be computed using the Fundamental Theorem of Calculus? (b) Assuming the Fundamental Theorem of Calculus could be applied to the integral above, what would it be? (c) Let e be a number so that 1> e > 0. Explain why the integrals dx, dx 2 can be computed using the Fundamental Theorem of Calculus. Compute them. (d) Determine lim dx + dx

Q: Evaluate, with an exact value, the definite integral º -1/1+a dx.

A:

Q: 97. To determine the value of the definite integral: 3 x - 3 x² - 6x + 10 a. Complete the square of…

A:

Q: let b be a constant. use definition to find  (integral 0 to b)(x+1)^2 dx.

A: Given: The expression of integral as ∫0bx+12dx, where b is a constant, To evaluate: The value of…

Q: (2) Compute the integral and then verify that you got the correct answer by differentiation. (a)…

A:

Q: 13) Calculate definite integral. Give answer as a fraction in lowest terms (x2 – 2x-3 + 3)dx

A: We will use integration rules

Q: оне dx 2 X√1+Lu² (x²) Secx sin 3x d x ۱/۱ ✓ で [H T =T TH ☑ M

A: Step 1:Step 2:

Q: Using the substitution u = sec(x), rewrite the integral tan7 (x) sec(x) dx as an integral involving…

A:

Q: 5. (12 points) Use the geometry or symmetry of integrals to evaluate the following definite…

A: Step 1:(a) The following formula of integration is known:∫a2−x2​dx=2x​a2−x2​+2a2​sin−1(ax​)+cwhere c…

Q: (c) [r³ sin (4r) da Using integration by parts to evaluate each integral. J (b) arcsin x dx re² (4¹)…

A: Integration by parts is a special technique of integration of two functions when they are…