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There are several classifications of linear Integral Equations. Some of them include; Voltera Integral Equations, Fredholm Linear Integral Equations, Fredholm-Voltera Integrodifferential. In the past, solutions of higher-order Fredholm-Volterra Integrodifferential Equations [FVIE] have been presented. However, this work uses a computational techniques premised on the third kind Chebyshev polynomials method. The performance of the results for distinctive degrees of approximation (M) of the trial solution is cautiously studied and comparisons have been additionally made between the approximate/estimated and exact/definite solution at different intervals of the problems under consideration. Modelled Problems have been provided to illustrate the performance and relevance of the techniques. However, it turned out that as M increases, the outcomes received after every iteration get closer to the exact solution in all of the problems considered. The results of the experiments are therefore visible from the tables of errors and the graphical representation presented in this work.

Objective: The objectives of this study was to identify the various microhabitats in which edible mushrooms grow; to identify their fruiting pattern time; and to relate the findings to their optimal exploitation in a Nigerian savannah. Methodology and Results: The mushrooms were collected at the onset to the end of the rainy season. Mushrooms at different stages of growth were handpicked; photographed at different resolutions and their microhabitats and the month in which they were found was recorded. Species identification was archived by carefully examining the attributes of the sporocarps such as colour, shape, size, texture of the cap; and presence or absence of gills, etc. T-Test and Diversity Indices were conducted on the data. Thirty-one (31) different edible mushroom species were found in the study area. They largely belong to the families of Agaricaceae, Lyophyllaceae and Polyporaceae. They are found in 18 different microhabitats, which include Arable Lands; Fallow lands; soils around dead Tree Stumps; Woods; and 14 different living tree species. The highest species richness (15) and species diversity (Shannon Diversity index, SDI: 2.54) was found under Parkia biglobosa tree. The second was Tamarindus indica, having 8 species with 1.95 SDI; followed by Decaying Wood where 6 different mushroom species were recorded with SDI of 1.57. Collectively, the exotic trees habited 8 mushroom species, while the indigenous trees habited 18, which was significantly (p-value = 0.0001) different. Decaying Wood has the highest peculiar species, which was 5; Fallow have 4 species; followed by Parkia biglobosa that has 3 species. Out of the total 31 species 21 were found in the year 2016 and 24 in 2017, while only13 species were found in both 2016 and 2017, but the difference was not statistically significant (p-value = 0.961). Conclusion and Application of results: The study area is rich in diverse edible mushroom species, which comprises mostly of those species belonging to the family Agaricaceae, Lyophyllaceae and Polyporaceae. The microhabitats of these mushrooms include arable lands currently under cultivation; abandoned fallow lands; soils around dead tree stumps; decaying woods; and 14 different living tree species. The result of this study has important information that can be an indispensable guide for proper exploitation of edible mushrooms in this region and elsewhere.

The purpose of this study was to investigate the potential benefits of substituting dietary fish meal with grasshopper meal on the growth performance of broiler chickens. The study was carried out in a mini-animal house of the Department of Biological Science, Federal University of Kashere, Gombe State, Nigeria. Seventy-two, 2-weeks old Arbor acres chicken strain were procured from May Farms, Gombe. The grasshoppers were collected using sweep net trapping method. They were oven dried and milled using local milling machine and incorporated into poultry diets by replacing dietary fishmeal at 0% (Control, A), 50% (B) and 100% (C). Each dietary treatment had 24 birds triplicates of eight birds per replicate in a completely randomized design. The birds were randomly allotted into pens demarcated with plywoods. The birds were fed the experimental diets throughout the six weeks period of the experiment and were subjected to similar managerial and dietary conditions during which time data was collected and used to evaluate weekly weight-gain, feed intake, feed conversion ratio, feed efficiency ratio and linear body measurements monitored. The weight-gain were significantly different (p<0.05) among the treatment groups where birds on Treatment C(1720.11±2.11 g) was highest followed by those on treatment B(1480.00±2.12 g) and the least mean final weekly weight gain of 1,287.98±1.20 g was observed in Treatment A; Also feed intake exhibited the same pattern of weight gain. For linear body measurements, the highest body length increase was recorded in Treatment C (21.39±1.01 cm) while the least was recorded in those on Treatment A, (15.49±1.10 cm). The same trend was observed for body width increase, thigh length increase, shank length increase and wing length increase. This study showed that dietary  grasshopper meal promoted growth of broiler chicken and so would conveniently replace dietary fishmeal. Therefore, establishmentof insect farms are highly recommended to produce enough grasshopper meal to meet the demands of poultry feed industries. Keywords: Arbor acres; growth parameters; dietary grasshopper; chicken body; liner measurement