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If 
and curve C is the arc of the curve y = x3 from (0, 0 ) to (2, 8), then the value of 
and curve C is the arc of the curve y = x3 from (0, 0 ) to (2, 8), then the value of - a)824
- b)824/21
- c)21/824
- d)0
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Ifand curve C is the arc of thecurve y = x3 from (0, 0 ) to (2, 8), th...
Since, C is the curve y = x3 from (0, 0) to (2, 8)
So, let x = t ⇒ y = t3
If
is the position vector of any point on C, then
or
or
At (0, 0) ⇒ t = x = 0 and at (2, 8) ⇒ t = 2
So, let x = t ⇒ y = t3
If
is the position vector of any point on C, thenor
or
At (0, 0) ⇒ t = x = 0 and at (2, 8) ⇒ t = 2
Most Upvoted Answer
Ifand curve C is the arc of thecurve y = x3 from (0, 0 ) to (2, 8), th...
Correct Answer :- b
Explanation : Since, C is the curve y = 3from (0, 0) to (2, 8)
So, let x = t ⇒ y = t3
If r is the position vector of any point on C, then
r(t) = xi + yj = ti +t3j
dr/dt = i + 3t2j
F = (t2 - t6)i + t4j
At (0, 0) ⇒ t = x = 0 and at (2, 8) ⇒ t = 2
∫F.dr = ∫C(F.dr/dt)dt
∫(0 to 2) [(t2 - t6)i + t4j] . (i + 3t2j)dt
∫(0 to 2) [(t2 - 2t6)dt]
= 824/21
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