Eduprobe
Question:
The value of g(1/2) is?
2π
π
π/2
π/4
Solution:
g(1/2)=lim_{h→0^+}∫_{1-h}^h t^{1/2}(1-t)^{1/2}dt=∫_0^1dt√t(1-t)=∫_0^1dt√(1/4-(t-1/2)^2)=sin⁻¹(t)|_0^1=sin⁻¹(1)-sin⁻¹(0)=π
2π
π
π/2
π/4
g(1/2)=lim_{h→0^+}∫_{1-h}^h t^{1/2}(1-t)^{1/2}dt=∫_0^1dt√t(1-t)=∫_0^1dt√(1/4-(t-1/2)^2)=sin⁻¹(t)|_0^1=sin⁻¹(1)-sin⁻¹(0)=π