Definite Integration

What is $\int_2^8|x-5| d x$ equal to?

Let $p=\int_a^b f(x) d x$ and $q=\int_a^b|f(x)| d x$. If $f(x)=e^{-x}$, then which one of the following is correct?

If $f(x)=2^x$, then what is $\int_2^{10} \frac{f^{\prime}(x)}{f(x)} d x$ equal to?

What is $\int_{-1}^1(3 \sin x-\sin 3 x) \cos ^2 x d x$ equal to?

Paragraph: Consider the integrals $\mathrm{I}_1=\int_0^x \frac{x d x}{1+\sin x} \text { and } \mathrm{I}_2=\int_0^\pi \frac{(\pi-x) d x}{1-\sin (\pi+x)}$ Question: What is the value of $\mathrm{I}_1+\mathrm{I}_2$ ?

If $\int_0^a[f(x)+f(-x)] d x=\int_{-a}^a g(x) d x$ then what is $g(x)$ equal to?

What is the value of $\int_0^{\pi / 4}\left(\tan ^3 x+\tan x\right) d x$ ?

Paragraph: Let $\mathrm{I}=\int_0^{\frac{\pi}{2}} \frac{f(x)}{g(x)} d x$, where $f(x)=\sin x$ and $g(x)=\sin x+\cos x+1$. Question: What is $\int_0^{\frac{\pi}{2}} \frac{d x}{g(x)}$ equal to?

Let $I=\int_{-2 \pi}^{2 \pi} \frac{\sin ^4 x+\cos ^4 x}{1+3^x} d x$ What is I equal to?

What is $\int_{-\pi / 2}^{\pi / 2}\left(e^{\cos x} \sin x+e^{\sin x} \cos x\right) d x$ equal to?

Paragraph: Let $\mathrm{I}=\int_0^{\frac{\pi}{2}} \frac{f(x)}{g(x)} d x$, where $f(x)=\sin x$ and $g(x)=\sin x+\cos x+1$. Question: What is I equal to?

Passage: Let $f(x)=\sin x$ and $g(x)-f(x)=f(4-x)$. Question: What is $\displaystyle\int_0^4\dfrac{f(4-x)}{g(4-x)}\,dx$ equal to ?