Question

Temperature of a rod is increased by moving x distance from origin and is given by equation T(x) = x^2 + 2x, where x is the distance and T(x) is change of temperature w.r.t distance. If, at x = 0, temperature is 40 C, find temperature at x=10.

(a) 473 C

(b) 472 C

(c) 474 C

(d) 475 C

The question was posed to me in homework.

Query is from Improper Integrals in section Integral Calculus of Engineering Mathematics

Answer 1

The correct option is (a) 473 C

The best I can explain: Temperature at distance x is,

T = ∫T(x) dx = ∫x^2 + 2x dx = ^x^3⁄3 + x^2 + C

At x=0 given T = 40 C

C = T(x = 0) = 40 C

At x= 10,

T(x = 10) = ^1000⁄3 + 100 + 43 = 473 C.