Question

Find the particular antiderivative of the following derivative that satisfies the given condition.

dR/dt=111/ t4​,

​R(1​)=25

Answer 1

Given differential equation lll dr dt 11 tu Mere dr dé is the first derivative of Rewith t, we can get R(E) by taking the Antiderivative to dr AR so, consider IL dt tu Tappily integration both sides with ty na re 111s tudt RCH any am ntl Sendt th + nti » R (A) - 111 t-un tc -441 » R (t)111 "{+3] to !! 1 / (+ 3) + c R(+) = CSScanned with CamScanner

Here is integral Constant tc :. RCH)= -11 -365 Given R(1)=25 ie.. when til R=25 So, when t=1 111 » RCO tc 3 (1) 3 4 25 11 -111 tc 3 CScanned with CamScanner

ca 25+ 111 LE cia (25) 37111 3 s . c in ist 3 981 c 3 c=6 기 so, consider -ll RCE) = t62, 3t3 +62 X R(6) - 111 3 is the required Antideriuative ECSscanned with CamScanner