" (vii) "int_(a)^(b)e^(-x)dx

int_(0)^(1)x e^(x)dx=

int_(-1)^(1)|x|e^(x)dx

int_(0)^(1000)e^(x-[x])dx

int_(0)^(1000)e^(x-[x])dx=

int(a)/(b+c.e^(x))dx=

Assertion (A) : Area enclosed by the curve y=e^(x^(3)) between the lines x = a, x = b and x - axis is int_(a)^(b) e^(x^(3)) dx . Reason (R ): e^(x^(3)) is an increasing functions.

Evaluate int_(a)^(b) e^(x) dx using the definition of a definite integral as the limit of a sum.

show that (a) int_(0) ^(2pi) sin ^(3) x dx = 0 , (b) int_(-1)^(1) e^(-x^(2)) dx = 2 int_(0)^(1) e^(-x^(2)) dx

inte^(x)(e^(x)-e^(-x))dx=