# Applications of integrals questions and answers

Recent questions in Applications of integrals
Applications of integrals

### Find integral $$\displaystyle\int{\frac{{\sqrt{{{x}^{{{2}}}-{9}}}}}{{{x}}}}{\left.{d}{x}\right.}$$

Applications of integrals

### Evaluate the integrals $$\displaystyle{\int_{{{0}}}^{{{\frac{{\pi}}{{{2}}}}}}}{\left[{\cos{{t}}}{i}-{\sin{{2}}}{t}{j}+{{\sin}^{{{2}}}{t}}{k}\right]}{\left.{d}{t}\right.}$$

Applications of integrals

### Evaluate the following integrals. $$\displaystyle\int{t}^{{{2}}}{\sin{{\left({3}{t}\right)}}}{\left.{d}{t}\right.}$$

Applications of integrals

### Evaluate the following integrals. $$\displaystyle{{\tan}^{{{7}}}{x}}{{\sec}^{{{4}}}{x}}{\left.{d}{x}\right.}$$

Applications of integrals

### Find the following integral. $$\displaystyle\int{\left({2}{t}^{{{2}}}-{1}\right)}^{{{2}}}{\left.{d}{t}\right.}$$

Applications of integrals

### Use an appropriate substitution and then a trigonometric substitution to evaluate the integrals. $$\displaystyle\int\sqrt{{{x}}}\sqrt{{{1}-{x}}}{\left.{d}{x}\right.}$$

Applications of integrals

### Evaluate the following integrals. Include absolute values. $$\displaystyle{\int_{{{0}}}^{{{1}}}}{\frac{{{y}{{\ln}^{{{4}}}{\left({y}^{{{2}}}+{1}\right)}}}}{{{y}^{{{2}}}+{1}}}}{\left.{d}{y}\right.}$$

Applications of integrals

### Evaluate the integral. $$\displaystyle{\int_{{{1}}}^{{{4}}}}{\frac{{{t}^{{{2}}}+{1}}}{{\sqrt{{{t}}}}}}{\left.{d}{t}\right.}$$

Applications of integrals

### Given that $$\displaystyle{\int_{{{4}}}^{{{9}}}}{f{{\left({x}\right)}}}{\left.{d}{x}\right.}={6}$$ and $$\displaystyle{\int_{{{9}}}^{{{k}}}}{f{{\left({x}\right)}}}{\left.{d}{x}\right.}=-{9}$$, find $$\displaystyle{\int_{{{k}}}^{{{4}}}}{f{{\left({x}\right)}}}{\left.{d}{x}\right.}$$.

Applications of integrals

### Evaluate the integral. $$\displaystyle{\int_{{{0}}}^{{{2}}}}{x}\sqrt{{{x}^{{{2}}}+{1}}}{\left.{d}{x}\right.}$$

Applications of integrals

### Evaluate the following integrals. $$\displaystyle{\int_{{{0}}}^{{{1}}}}{2}{x}{{\tan}^{{-{1}}}{\left({x}^{{{2}}}\right)}}{\left.{d}{x}\right.}$$

Applications of integrals

### Find the following integral. $$\displaystyle\int{\left({1}+{3}{t}\right)}{t}^{{{2}}}{\left.{d}{t}\right.}$$

Applications of integrals

### Evaluate $$\displaystyle\int{{\sin}^{{{5}}}{x}}{\left.{d}{x}\right.}$$.

Applications of integrals

### Evaluate the following definite integral. $$\displaystyle{\int_{{{1}}}^{{{3}}}}{\frac{{{3}}}{{{x}^{{{3}}}}}}+{2}{x}{\left.{d}{x}\right.}$$

Applications of integrals

### Evaluate the integral. $$\displaystyle{\int_{{{3}}}^{{{4}}}}{\left({4}{x}-{\frac{{{2}}}{{{x}^{{{2}}}}}}\right)}{\left.{d}{x}\right.}$$

Applications of integrals

### Evaluate the following integrals. $$\displaystyle{e}^{{{2}{x}}}{\cos{{\left({3}{x}\right)}}}{\left.{d}{x}\right.}$$

Applications of integrals

### Find all possible functions with the given derivative. $$\displaystyle{y}^{{{p}{r}{i}{m}{e}}}={5}-{\frac{{{2}}}{{{x}^{{{2}}}}}}$$ y=?

Applications of integrals

### Evaluate the integral. $$\displaystyle{\int_{{{0}}}^{{{w}}}}{e}^{{-{2}{a}{\left|{t}\right|}}}{\left.{d}{t}\right.}$$

Applications of integrals