If the curve x^2 = 4y intersects the line y = 2(x+6) at (a, b) in 2^(nd) quadrant, then ∫ x^4/1+5^x dx x ∈ to (a, b) is

Question

If the curve \(x^{2}=4 y\) intersects the line \(y=2(x+6)\) at (a, b) in \(2^{\text {nd }}\) quadrant, then \(\int_\limits{a}^{b} \frac{x^{4}}{1+5^{x}} d x\) is

(1) \(\frac{512}{5}\)

(2) \(\frac{1024}{5}\)

(3) \(\frac{32}{5}\)

(4) \(\frac{16}{5}\)

Answer 1

Answer is: (2) \(\frac{1024}{5}\) 

\(=\int_\limits{0}^{4}\left(\frac{x^{4}}{1+5^{x}}+\frac{x^{4}}{1+5^{-x}}\right) d x\)

\(=\int_\limits{0}^{4} x^{4} d x=\frac{x^{5}}{5}=\frac{4^{5}}{5}=\frac{1024}{5}\)