3. (a) What is the smallest, positive value of $x$ so that \(\int_0^x \cos(t)dt = 0\)? (b) Use a substitution to evaluate the integral \(\int_0^{\sqrt{\frac{\pi}{2}}} x \cos(x^2)dx\).
Added by Christian M.
Close
Step 1
Step 1: To find the smallest positive value of x such that cos(t) dt = 0, we need to solve the equation ∫cos(t) dt = 0. Show more…
Show all steps
Your feedback will help us improve your experience
Supreeta N and 53 other Calculus 1 / AB educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Please show detailed step-by-step solution. Thanks CON3303 Tutorial 11:Integration by parts,integration by substitution,integration using partial fractions 3.Find the integral of each of the following: a. ∫(x+3)/((x+1)(x+2)) dx b. ∫(x-9)/(2x^2-3x+1) dx c. ∫(x^2+3)/(x^2+3x) dx d. ∫x^3/(x^2+3x+2) dx e. ∫(2x^2+7x+7)/(x+2) dx f. ∫[1 to 3] (x-1)/(4x^2+x) dx
Supreeta N.
3a
Khushbu R.
(a) Make the indicated $u$ -substitution, and then use the Endpaper Integral Table to evaluate the integral. (b) If you have a CAS, use it to evaluate the integral, and then confirm that the result is equivalent to the one that you found in part (a). $$\int \ln (3 x+1) d x, u=3 x+1$$
PRINCIPLES OF INTEGRAL EVALUATION
Using Computer Algebra Systems and Tables of Integrals
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD