Suppose f is a continuous real-valued function such that 3x⁵ + 96 = ∫xc f(y)dy for each x ∈ R, where c is a constant. What is the value of c?
- 2
- -2
- -1
- None of these
Explanation
Given: 3x⁵ + 96 = ∫_c^x f(y) dy for all x
1) Differentiate both sides w.r.t x
Use Fundamental Theorem of Calculus: d/dx ∫_c^x f(y) dy = f(x)
So: d/dx [3x⁵ + 96] = f(x)
→ f(x) = 15x⁴
2) Put x = c
LHS: 3c⁵ + 96
RHS: ∫_c^c f(y) dy = 0
So 3c⁵ + 96 = 0
→ c⁵ = -32
→ c = -2
Last verified on 04-06-2026
Related MCQs
- {1}
- {-1}
- {0}
- None of these
اس سوال کو وضاحت کے ساتھ پڑھیں
- -72
- -60
- -48
- None of these
اس سوال کو وضاحت کے ساتھ پڑھیں
