Evaluate \(\int_0^3 2\,dx\).

What is \(\int_5^5 (x^2+1)\,dx\)?

Use the order-reversal property to rewrite \(\int_4^1 x^2\,dx\) with lower limit \(1\) and upper limit \(4\).

If \(\int_1^6 f(x)\,dx=9\), find \(\int_6^1 f(x)\,dx\).

Evaluate \(\int_0^2 x\,dx\).

Evaluate \(\int_1^3 (2x+1)\,dx\).

Evaluate \(\int_{-1}^{2} (3x^2-4)\,dx\).

Evaluate \(\int_0^4 \sqrt{x}\,dx\).

Evaluate \(\int_1^2 (x^3-2x+5)\,dx\).

Evaluate \(\int_0^\pi \sin x\,dx\).

The velocity of a particle is \(v(t)=6t-2\) metres per second. Find its displacement from \(t=1\) to \(t=4\).

Find the signed area \(\int_{-2}^{2} x^3\,dx\), and explain why the value is reasonable.

Find the area between \(y=x+2\) and the \(x\)-axis from \(x=-1\) to \(x=3\).

Find the area between \(y=4-x^2\) and the \(x\)-axis from \(x=-2\) to \(x=2\).

Find \(k\) if \(\int_0^2 kx\,dx=12\).

Find \(a>0\) such that \(\int_0^a 3x^2\,dx=24\).

For which values of \(c\) is \(\int_{-c}^{c} (x^2-1)\,dx=0\)?

A student says \(\int_{-1}^{1} x^2\,dx=0\) because the limits are symmetric. Identify the error and find the correct value.

Find the total area between \(y=x\) and the \(x\)-axis from \(x=-2\) to \(x=3\).

Suppose \(f(x)\ge0\) on \([0,2]\), \(f(x)\le0\) on \([2,5]\), \(\int_0^2 f(x)\,dx=7\), and \(\int_2^5 f(x)\,dx=-4\). Find the signed area and the total area from \(0\) to \(5\).