(a) Find ? sin x cos x dx using the substitution u = sin x. (b) Find ? sin x cos x dx using the substitution u = cos x. (c) Show that the two results are equal. (a) ? sin x cos x dx = [ ] (b) ? sin x cos x dx = [ ] (c) Substitute sin^2 x = 1 - cos^2 x into your answer for (a) and simplify.
Added by Juan P.
Close
Your feedback will help us improve your experience
Sri K and 55 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
Evaluate $\int \sin x \cos x d x$ by four methods: $$\begin{array}{l}{\text { (a) the substitution } u=\cos x} \\ {\text { (b) the substitution } u=\sin x} \\ {\text { (c) the identity } \sin 2 x=2 \sin x \cos x} \\ {\text { (d) integration by parts }}\end{array}$$ Explain the different appearances of the answers.
Techniques of Integration
Trigonometric Integrals
Find the indefinite integral shown below using the given method ∫ sin(x) cos(x) dx (a) substitution where u = sin(x) sin(x)^2 / 2 + C (b) substitution where u = cos(x) -cos(x)^2 / 2 + C (c) integration by parts + C (d) using the identity sin(2x) = 2 sin(x) cos(x) + C
Suman Saurav T.
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD