Calculus

Integration Techniques

Integration Techniques: Level 2 Challenges

         

π2π2[esin(x)cos(x)] dx=a1a,   a>0,     a= ?\large \int_{-\frac \pi 2 }^{\frac \pi 2 } \bigg [ e^{ \sin(x)} \cos (x )\bigg ] \ dx = a - \frac 1 a, \ \ \ a > 0, \ \ \ \ \ a = \ ?

1ax1x+xdx=4\large\int_{1}^{a}\dfrac{x-1}{x+\sqrt{x}}dx=4

Let a>1a>1 be a constant satisfying the equation above. What is the value of a2+a+1\large a^2+a+1?

Evaluate the following integral

sin(x)cos3(x)dx\large\displaystyle \int \dfrac{\sin(x)}{\cos^3(x)} \, \Bbb{d}x

02x1(x1)2dx=? \int_0^2 x \sqrt{1-(x-1)^2} \, dx = \, ?

Give your answer to 2 decimal places.

Evaluate the indefinite integral below.

dx1+ex\large \int \frac{dx}{1 + e^{-x}}

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