CUET and UG exam CUET UG 2025 Mock Test Series Mathematics Integral Calculus Application of Integrals
If a curve y = f(x) passes through the point (1, 2) and satisfies \({\rm{x}}\frac{{{\rm{dy}}}}{{{\rm{dx}}}}\,{\rm{ + }}\,{\rm{y}}\,{\rm{ = }}\,{\rm{b}}{{\rm{x}}^{\rm{4}}}\), then for what value of b, \(\int\limits_{\rm{1}}^{\rm{2}} {{\rm{f}}\left( {\rm{x}} \right)} \,{\rm{dx}}\,{\rm{ = }}\,\frac{{{\rm{62}}}}{{\rm{5}}}\) ?
1
10
2
\(\frac{{31}}{5}\)
3
5
4
\(\frac{{62}}{5}\)