Question
Solve $\int_{0}^{x} t y(t) d t=x^{2} y(x) .$
Step 1
Using Leibniz's rule for differentiating an integral, we have: $\frac{d}{dx} \int_{0}^{x} t y(t) dt = \frac{d}{dx} (x^2 y(x))$ On the left side, we get: $y(x) \cdot x = 2x y(x) + x^2 y'(x)$ Show more…
Show all steps
Your feedback will help us improve your experience
Kian Manafi and 89 other Calculus 2 / BC 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
Find $d y / d x$ $y=\int_{0}^{x^{2}} e^{2^{2}} d t$
The Definite Integral
Fundamental Theorem of Calculus
Find $d y / d x$ $$ y=\int_{1}^{x} \frac{1}{t} d t, \quad x>0 $$
Integrals
The Fundamental Theorem of Calculus
Find $d y / d x.$ $$y=\int_{1}^{x} \frac{1}{t} d t, \quad x>0$$
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD