point) Integrals Resulting in Inverse Trigonometric Functions_ Input the antiderivative of the integrand and limits of integration: Then evaluate the definite integral. dx 7
Added by Michelle F.
Close
Step 1
Step 1: Recognize that d/dx(arcsin x) = 1/sqrt(1 - x^2), so an antiderivative is F(x) = arcsin(x). Show more…
Show all steps
Your feedback will help us improve your experience
Syed Mustafa and 79 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
Integrals Resulting in Inverse Trigonometric Functions The table below contains the derivatives of the inverse trigonometric functions that arise frequently in integration: With help from the table above, evaluate the following indefinite integral. Hint: a simple substitution may help. Note: answer should be in terms of t only.
Suman Saurav T.
Evaluate the given indefinite integral by a trigonometric substitution where appropriate. You should be able to evaluate some of the integrals without a substitution. $$ \int x \sqrt{x^{2}+7} d x $$
Techniques of Integration
Trigonometric Substitutions
Make a substitution to express the integrand as a rational function and then evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) ex (ex − 2)(e2x + 1) dx Evaluate the integral using the indicated trigonometric substitution. (Use C for the constant of integration.) x3 x2 + 49 dx , x = 7 tan(θ)
Drew S.
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD