The solution of the previous three problems is $\sum _ { n = 1 } ^ { \infty } c _ { n } X _ { n } ( x ) e ^ { - \lambda _ { n } k t }$ , where $X _ { n }$ and $\lambda _ { n }$ are given in the previous problem and
A) $c _ { n } = \int _ { 0 } ^ { L } f ( x ) d x$
B) $c _ { n } = \int _ { 0 } ^ { L } f ( x ) X _ { n } ( x ) d x$
C) $c _ { n } = \int _ { 0 } ^ { L } f ( x ) X _ { n } ( x ) d x / \int _ { 0 } ^ { L } X _ { n } ( x ) d x$
D) $c _ { n } = \int _ { 0 } ^ { L } X _ { n } ^ { 2 } ( x ) d x / \int _ { 0 } ^ { L } f ( x ) X _ { n } ( x ) d x$
E) $c _ { n } = \int _ { 0 } ^ { L } f ( x ) X _ { n } ( x ) d x / \int _ { 0 } ^ { L } X _ { n } ^ { 2 } ( x ) d x$

Question

Quizplus · Accepted Answer

The Answer of The solution of the previous three problems is $\sum _ { n = 1 } ^ { \infty } c _ { n } X _ { n } ( x ) e ^ { - \lambda _ { n } k t }$ , where $X _ { n }$ and $\lambda _ { n }$ are given in the previous problem and
A) $c _ { n } = \int _ { 0 } ^ { L } f ( x ) d x$
B) $c _ { n } = \int _ { 0 } ^ { L } f ( x ) X _ { n } ( x ) d x$
C) $c _ { n } = \int _ { 0 } ^ { L } f ( x ) X _ { n } ( x ) d x / \int _ { 0 } ^ { L } X _ { n } ( x ) d x$
D) $c _ { n } = \int _ { 0 } ^ { L } X _ { n } ^ { 2 } ( x ) d x / \int _ { 0 } ^ { L } f ( x ) X _ { n } ( x ) d x$
E) $c _ { n } = \int _ { 0 } ^ { L } f ( x ) X _ { n } ( x ) d x / \int _ { 0 } ^ { L } X _ { n } ^ { 2 } ( x ) d x$

The Solution of the Previous Three Problems Is ∑n=1∞cnXn(x)e−λnkt\sum _ { n = 1 } ^ { \infty } c _ { n } X _ { n } ( x ) e ^ { - \lambda _ { n } k t }∑n=1∞​cn​Xn​(x)e−λn​kt

The Solution of the Previous Three Problems Is $\sum _ { n = 1 } ^ { \infty } c _ { n } X _ { n } ( x ) e ^ { - \lambda _ { n } k t }$