Advertisements
Advertisements
Question
Evaluate : `int_1^3 (x^2 + 3x + e^x) dx` as the limit of the sum.
Advertisements
Solution
APPEARS IN
RELATED QUESTIONS
Evaluate the following definite integrals as limit of sums.
`int_0^5 (x+1) dx`
Evaluate the following definite integrals as limit of sums.
`int_2^3 x^2 dx`
Evaluate the following definite integrals as limit of sums.
`int_1^4 (x^2 - x) dx`
Evaluate the definite integral:
`int_(pi/6)^(pi/3) (sin x + cosx)/sqrt(sin 2x) dx`
Evaluate the definite integral:
`int_0^(pi/2) sin 2x tan^(-1) (sinx) dx`
Prove the following:
`int_1^3 dx/(x^2(x +1)) = 2/3 + log 2/3`
Prove the following:
`int_(-1)^1 x^17 cos^4 xdx = 0`
`int (cos 2x)/(sin x + cos x)^2dx` is equal to ______.
If f (a + b - x) = f (x), then `int_a^b x f(x )dx` is equal to ______.
\[\int\frac{1}{x} \left( \log x \right)^2 dx\]
\[\int\limits_0^1 \left( x e^x + \cos\frac{\pi x}{4} \right) dx\]
Using L’Hospital Rule, evaluate: `lim_(x->0) (8^x - 4^x)/(4x
)`
Evaluate:
`int (sin"x"+cos"x")/(sqrt(9+16sin2"x")) "dx"`
Evaluate `int_(-1)^2 (7x - 5)"d"x` as a limit of sums
Evaluate the following as limit of sum:
`int_0^2 "e"^x "d"x`
Evaluate the following:
`int_0^1 (x"d"x)/sqrt(1 + x^2)`
The value of `int_(-pi)^pi sin^3x cos^2x "d"x` is ______.
If f" = C, C ≠ 0, where C is a constant, then the value of `lim_(x -> 0) (f(x) - 2f (2x) + 3f (3x))/x^2` is
Left `f(x) = {{:(1",", "if x is rational number"),(0",", "if x is irrational number"):}`. The value `fof (sqrt(3))` is
`lim_(n rightarrow ∞)1/2^n [1/sqrt(1 - 1/2^n) + 1/sqrt(1 - 2/2^n) + 1/sqrt(1 - 3/2^n) + ...... + 1/sqrt(1 - (2^n - 1)/2^n)]` is equal to ______.
