Definite integrals practice problems
Evaluate with the Fundamental Theorem of Calculus: F(b) − F(a). 30 problems with worked solutions; in 30 of them every equation is proved by a computer algebra system.
Evaluate \( \displaystyle \int_{2}^{3} 2 - 2 x \, dx \).
Evaluate \( \displaystyle \int_{1}^{3} 4 x - 2 \, dx \).
Evaluate \( \displaystyle \int_{-2}^{1} x \left(x^{2} + 1\right)^{3} \, dx \).
Evaluate \( \displaystyle \int_{-2}^{3} 4 x^{3} + 3 x^{2} - 2 \, dx \).
Evaluate \( \displaystyle \int_{1}^{9} 3 \sqrt{x} - 2 \, dx \).
Evaluate \( \displaystyle \int_{0}^{3} - 3 x^{3} - 4 x^{2} - 3 x + 1 \, dx \).
Evaluate \( \displaystyle \int_{0}^{\frac{\pi}{2}} 2 \sin{\left(x \right)} + 2 \cos{\left(x \right)} \, dx \).
Evaluate \( \displaystyle \int_{1}^{2} x \left(x^{2} + 1\right)^{3} \, dx \).
Evaluate \( \displaystyle \int_{1}^{3} 2 x^{2} - 2 x + 3 \, dx \).
Evaluate \( \displaystyle \int_{1}^{9} 4 \sqrt{x} + 2 \, dx \).
Evaluate \( \displaystyle \int_{1}^{3} x \left(x^{2} + 1\right)^{2} \, dx \).
Evaluate \( \displaystyle \int_{1}^{4} 2 \sqrt{x} + 2 \, dx \).
Evaluate \( \displaystyle \int_{0}^{2} x + e^{x} \, dx \).
Evaluate \( \displaystyle \int_{0}^{1} 3 x^{2} - 3 x - 3 \, dx \).
Evaluate \( \displaystyle \int_{0}^{\frac{\pi}{2}} 3 \sin{\left(x \right)} + \cos{\left(x \right)} \, dx \).
Evaluate \( \displaystyle \int_{1}^{9} x + \frac{3}{x} \, dx \).
Evaluate \( \displaystyle \int_{-2}^{3} x \left(x^{2} + 1\right)^{2} \, dx \).
Evaluate \( \displaystyle \int_{0}^{\pi} 3 \sin{\left(x \right)} - 3 \cos{\left(x \right)} \, dx \).
Evaluate \( \displaystyle \int_{1}^{2} x \left(x^{2} + 1\right)^{2} \, dx \).
Evaluate \( \displaystyle \int_{-1}^{2} x + e^{2 x} \, dx \).
Evaluate \( \displaystyle \int_{-1}^{3} x + e^{x} \, dx \).
Evaluate \( \displaystyle \int_{-2}^{3} x + e^{2 x} \, dx \).
Evaluate \( \displaystyle \int_{0}^{\frac{\pi}{3}} 3 \sin{\left(x \right)} + 2 \cos{\left(x \right)} \, dx \).
Evaluate \( \displaystyle \int_{1}^{4} x + \frac{5}{x} \, dx \).
Evaluate \( \displaystyle \int_{-1}^{0} x + e^{x} \, dx \).
Evaluate \( \displaystyle \int_{1}^{2} x + \frac{3}{x} \, dx \).
Evaluate \( \displaystyle \int_{1}^{2} \sqrt{x} - 1 \, dx \).
Evaluate \( \displaystyle \int_{1}^{e} 2 \sqrt{x} - 2 \, dx \).
Evaluate \( \displaystyle \int_{1}^{2} 2 \sqrt{x} - 1 \, dx \).
Evaluate \( \displaystyle \int_{1}^{2} 3 \sqrt{x} - 2 \, dx \).