Why integral left parenthesis x squared space d y space plus space 2 x y space d x right parenthesis is equal to x squared y space plus space straight C and not 2 x squared y space plus space straight C?

Asked by rishabhsankla1 | 6th Sep, 2020, 11:14: PM

Expert Answer:

To find the integral of x2 dy + 2xy dx
If space we space take space derivative space of space straight x squared straight y space straight i. straight e. space straight d over dx open parentheses straight x squared straight y close parentheses space then space we space get
straight d over dx open parentheses straight x squared straight y close parentheses equals straight x squared dy over dx plus 2 xy
straight d open parentheses straight x squared straight y close parentheses equals straight x squared dy plus 2 xy space dx
Therefore comma space integral straight x squared dy plus 2 xy space dx equals integral straight d open parentheses straight x squared dy plus 2 xy space dx close parentheses space equals space straight x squared straight y plus straight C

Answered by Renu Varma | 7th Sep, 2020, 12:34: PM

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