[amp_mcq option1=”0″ option2=”a” option3=”2a” option4=”$$2\\int_0^{\\text{a}} {{\\text{f}}\\left( {\\text{x}} \\right){\\text{dx}}} $$” correct=”option1″]<\/p>\n
The correct answer is $\\boxed{\\text{D}}$.<\/p>\n
An even function is a function $f$ such that $f(-x) = f(x)$ for all $x$.<\/p>\n
The integral $\\int_{-a}^a f(x) dx$ is the area under the curve $y=f(x)$ between $x=-a$ and $x=a$.<\/p>\n
If $f$ is even, then the graph of $y=f(x)$ is symmetric about the $y$-axis. This means that the area under the curve between $x=-a$ and $x=a$ is the same as the area under the curve between $x=0$ and $x=a$.<\/p>\n
Therefore, $\\int_{-a}^a f(x) dx = 2 \\int_0^a f(x) dx$.<\/p>\n","protected":false},"excerpt":{"rendered":"
[amp_mcq option1=”0″ option2=”a” option3=”2a” option4=”$$2\\int_0^{\\text{a}} {{\\text{f}}\\left( {\\text{x}} \\right){\\text{dx}}} $$” correct=”option1″]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[690],"tags":[],"class_list":["post-20260","post","type-post","status-publish","format-standard","hentry","category-calculus","no-featured-image-padding"],"yoast_head":"\n